Solve Each Inequality. Graph the Solution Set on a Number Line. 1

Home , Number line

Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

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1-6 Solving Compound and Absolute Value Inequalities

Solve each inequality. Graph the solution set on 7. a number line. 1. ANSWER:

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11. MONEY Khalid is considering several types of paint for his bedroom. He estimates that he will need 5. between 2 and 3 gallons. The table at the right shows the price per gallon for each type of paint Khalid is ANSWER: considering. Write a compound inequality and determine how much he could be spending.

6. ANSWER:

ANSWER: 7. between $43.96 and $77.94 ANSWER: Solve each inequality. Graph the solution set on a number line. 12. ANSWER: eSolutions Manual - Powered by Cognero Page 1 8. ANSWER:

13. ANSWER: 9. ANSWER:

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15. or ANSWER: 11. MONEY Khalid is considering several types of paint for his bedroom. He estimates that he will need between 2 and 3 gallons. The table at the right shows the price per gallon for each type of paint Khalid is considering. Write a compound inequality and 16. determine how much he could be spending. ANSWER:

17. ANSWER: ANSWER: between $43.96 and $77.94

Solve each inequality. Graph the solution set on a number line. 18. 12. ANSWER: ANSWER:

19. 13. ANSWER: ANSWER:

14. or 20. ANSWER: ANSWER:

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ANSWER: 22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the 17. height of a woman given the length of her femur bone. ANSWER: b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value inequality that describes the woman’s height in centimeters. ANSWER: 18. a. ANSWER: b.

Write an absolute value inequality for each graph. 23. 19. ANSWER: ANSWER:

24. ANSWER:

20. ANSWER: 25. ANSWER:

21. 26. ANSWER: ANSWER:

27. ANSWER: 22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 28. centimeters. Write an inequality to represent the ANSWER: height of a woman given the length of her femur

bone. b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value 29. inequality that describes the woman’s height in centimeters. ANSWER:

ANSWER: a. b. 30. ANSWER: Write an absolute value inequality for each graph.

23. 31. DOGS The Labrador retriever is one of the most ANSWER: recognized and popular dogs kept as a pet. Using the information given, write a compound inequality to describe the range of healthy weights for a fully grown female Labrador retriever.

24. ANSWER:

ANSWER: 25.

ANSWER: 32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is greater than the measure of either of its 26. corresponding remote interior angles. Write two inequalities to express the relationships among the ANSWER: measures of the angles of ABC.

27.

ANSWER:

28. Solve each inequality. Graph the solution set on ANSWER: a number line. 33. ANSWER: 29. ANSWER:

34. 30. ANSWER: ANSWER:

31. DOGS The Labrador retriever is one of the most recognized and popular dogs kept as a pet. Using the 35. information given, write a compound inequality to describe the range of healthy weights for a fully ANSWER: grown female Labrador retriever.

36.

ANSWER: ANSWER:

32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is greater than the measure of either of its 37. corresponding remote interior angles. Write two ANSWER: inequalities to express the relationships among the

measures of the angles of ABC.

38. ANSWER:

ANSWER:

Solve each inequality. Graph the solution set on a number line. 33. 39.

ANSWER: ANSWER:

34.

ANSWER: 40.

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35. ANSWER: Write an algebraic expression to represent each verbal expression. 41. numbers that are at least 4 units from –5 ANSWER: 36.

ANSWER:

42. numbers that are no more than unit from 1

ANSWER:

37. ANSWER: 43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER:

38. 44. AUTO RACING NASCAR rules stipulate that a ANSWER: car must conform to a set of 32 templates, each shaped to fit a different contour of the car. When a template is placed on a car, the gap between it and the car cannot exceed the specified tolerance. Each template is marked on its edge with a colored line that indicates the tolerance for the template.

39.

ANSWER:

a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write 40. an absolute value inequality for templates with each line color. ANSWER: b. Find the acceptable lengths for that part of a car if the template has each line color. c. Graph the solution set for each line color on a number line. d. The tolerance of which line color includes the tolerances of the other line colors? Write an algebraic expression to represent Explain your reasoning. each verbal expression. 41. numbers that are at least 4 units from –5 ANSWER: a. ANSWER:

b. 42. numbers that are no more than unit from 1

ANSWER: c.

43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER:

d. Red; the red line color has the smallest tolerance, AUTO RACING 44. NASCAR rules stipulate that a , so the other line colors would be car must conform to a set of 32 templates, each shaped to fit a different contour of the car. When a well within their tolerances. template is placed on a car, the gap between it and Solve each inequality. Graph the solution set on the car cannot exceed the specified tolerance. Each a number line. template is marked on its edge with a colored line 45. that indicates the tolerance for the template. ANSWER:

46.

a. Suppose a certain template is 24.42 inches long. ANSWER: Use the information in the table at the right to write an absolute value inequality for templates with each line color. b. Find the acceptable lengths for that part of a car if the template has each line color. 47. c. Graph the solution set for each line color on a ANSWER: number line. d. The tolerance of which line color includes the tolerances of the other line colors? Explain your reasoning. ANSWER: 48. a . ANSWER:

49. c. ANSWER:

50.

d. Red; the red line color has the smallest tolerance, ANSWER: , so the other line colors would be well within their tolerances.

Solve each inequality. Graph the solution set on a number line. 51. HEALTH Hypoglycemia (low blood sugar) and 45. hyperglycemia (high blood sugar) are potentially dangerous and occur when a person’s blood sugar ANSWER: fluctuates by more than 38 mg from the normal blood sugar level of 88 mg. Write and solve an absolute value inequality to describe blood sugar levels that are considered potentially dangerous. ANSWER: 46. ANSWER: 52. AIR TRAVEL The airline on which Drew is flying has weight restrictions for checked baggage. Drew is checking one bag. a. Describe the range of weights that would classify 47. Drew’s bag as free, $25, $50, and unacceptable. b. If Drew’s bag weighs 68 pounds, how much will ANSWER: he pay to take it on the plane?

48. ANSWER:

ANSWER:

a. 49. b. $25

ANSWER: 53. ERROR ANALYSIS David and Sarah are solving . Is either of them correct? Explain your reasoning.

50. ANSWER: ANSWER: Sample answer: David; when Sarah converted the absolute value into two inequalities, she mistakenly switched 51. HEALTH Hypoglycemia (low blood sugar) and the inequality symbols. hyperglycemia (high blood sugar) are potentially dangerous and occur when a person’s blood sugar 54. CHALLENGE Solve fluctuates by more than 38 mg from the normal blood sugar level of 88 mg. Write and solve an absolute ANSWER: value inequality to describe blood sugar levels that x < 0 are considered potentially dangerous. REASONING Determine whether each ANSWER: statement is true or false . If false, provide a counterexample. 55. The graph of a compound inequality involving an and 52. AIR TRAVEL The airline on which Drew is flying statement is bounded on the left and right by two has weight restrictions for checked baggage. Drew is values of x.

checking one bag. ANSWER: a. Describe the range of weights that would classify False; sample answer: the graph of Drew’s bag as free, $25, $50, and unacceptable. x > 2 and x > 5 is a ray bounded only on one end. b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane? 56. The graph of a compound inequality involving an or statement contains a region of values that are not solutions. ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the ANSWER: given statement true. a. ANSWER: b. $25 True

53. ERROR ANALYSIS David and Sarah are solving 58. WRITING IN MATH An alternate definition of . Is either of them absolute value is to define as the distance correct? Explain your reasoning. between a and b on the number line. Explain how this definition can be used to solve inequalities of the form .

ANSWER:

Sample answer: represents the distance between some unknown value of the ANSWER: variable x and a point c on the number line. The Sample answer: David; when Sarah converted the solution set of the inequality is the set of all numbers absolute value into two inequalities, she mistakenly such that the distance from the numbers to c is less switched than r units. Use a number line to find the numbers the inequality symbols. that are r units from c in either direction.

54. CHALLENGE Solve 59. REASONING The graphs of the solutions of two different absolute value inequalities are shown. ANSWER: Compare and contrast the absolute value inequalities. x < 0

REASONING Determine whether each statement is true or false . If false, provide a counterexample. 55. The graph of a compound inequality involving an and ANSWER: statement is bounded on the left and right by two Sample answer: The graph on the left indicates a values of x. solution set from –3 to 5. The graph on the right indicates a solution ANSWER: set of all numbers less than or equal to False; sample answer: the graph of –3 or greater than or equal to 5. x > 2 and x > 5 is a ray bounded only on one end. 60. OPEN ENDED Write an absolute value inequality 56. The graph of a compound inequality involving an or with a solution of statement contains a region of values that are not ANSWER: solutions. Sample answer: ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line. 61. WHICH ONE DOESN’T BELONG? Identify the 57. The graph of a compound inequality involving an and compound inequality that is not the same as the other statement includes values that make all parts of the three. Explain your reasoning. given statement true. ANSWER: True 58. WRITING IN MATH An alternate definition of ANSWER: absolute value is to define as the distance Each of these has a non-empty solution set except between a and b on the number line. Explain how for x > 5 and x < 1. There are no values of x that are this definition can be used to solve inequalities of the simultaneously greater than 5 and less than 1.

form . 62. WRITING IN MATH Summarize the difference ANSWER: between and compound inequalities and or compound inequalities. Sample answer: represents the distance between some unknown value of the ANSWER: variable x and a point c on the number line. The Sample answer: A compound inequality that contains solution set of the inequality is the set of all numbers and is true if and only if both individual inequalities such that the distance from the numbers to c is less are true, while an inequality containing or only needs than r units. Use a number line to find the numbers one of the individual inequalities to be true. that are r units from c in either direction. 63. Which of the following best describes the graph of 59. REASONING The graphs of the solutions of two the equations below? different absolute value inequalities are shown. Compare and contrast the absolute value inequalities. A The lines have the same x-intercept. B The lines have the same y-intercept. C The lines are parallel. D The lines are perpendicular. ANSWER: ANSWER: Sample answer: The graph on the left indicates a C solution set from –3 to 5. The

graph on the right indicates a solution 64. SAT/ACT Find an expression equivalent

set of all numbers less than or equal to –3 or greater than or equal to 5. to 60. OPEN ENDED Write an absolute value inequality with a solution of F ANSWER:

Sample answer: G

61. WHICH ONE DOESN’T BELONG? Identify the compound inequality that is not the same as the other J three. Explain your reasoning.

ANSWER: ANSWER: Each of these has a non-empty solution set except K for x > 5 and x < 1. There are no values of x that are simultaneously greater than 5 and less than 1. 65. GRIDDED RESPONSE How many cubes that measure 4 centimeters on each side can be placed 62. WRITING IN MATH Summarize the difference completely inside the box below? between and compound inequalities and or compound inequalities. ANSWER: Sample answer: A compound inequality that contains and is true if and only if both individual inequalities are true, while an inequality containing or only needs ANSWER: one of the individual inequalities to be true. 60 63. Which of the following best describes the graph of the equations below? 66. Which graph represents the solution set for

A A The lines have the same x-intercept. B The lines have the same y-intercept. B C The lines are parallel. D The lines are perpendicular. C ANSWER: D C ANSWER: A 64. SAT/ACT Find an expression equivalent 67. HEALTH The National Heart Association to recommends that less than 30% of a person’s total daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old F whose average caloric intake is between 2500 and 3300 Calories. a G . Write an inequality that represents the suggested fat intake for the person. b. What is the greatest suggested fat intake for the H person? ANSWER: J a. b.110g

K 68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. Her plane ticket is $375, and the hotel is $85 per ANSWER: night. K a. Let f represent the cost of food for one day. Write an inequality to represent this situation. 65. GRIDDED RESPONSE How many cubes that b. Solve the inequality and interpret the solution. measure 4 centimeters on each side can be placed ANSWER: completely inside the box below? a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER: ANSWER: 60 66. Which graph represents the solution set for 70.

A ANSWER:

C 71. D ANSWER: ANSWER: A Name the property illustrated by each 67. HEALTH The National Heart Association statement. recommends that less than 30% of a person’s total 72. If then daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old ANSWER: whose average caloric intake is between 2500 and Addition (=) 3300 Calories. a. Write an inequality that represents the suggested fat intake for the person. 73. If and then b. What is the greatest suggested fat intake for the person? ANSWER: ANSWER: Transitive (=) a. b.110g 74. If then

68. TRAVEL Maggie is planning a 5-day trip to a family ANSWER: reunion. She wants to spend no more than $1000. Assoc. (+) Her plane ticket is $375, and the hotel is $85 per night. a. Let f represent the cost of food for one day. Write an inequality to represent this situation. b. Solve the inequality and interpret the solution. ANSWER: a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER:

70.

ANSWER:

71.

ANSWER:

Name the property illustrated by each statement. 72. If then ANSWER: Addition (=)

73. If and then

ANSWER: Transitive (=)

74. If then

ANSWER: Assoc. (+) Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

2. ANSWER:

3. or ANSWER:

4. or ANSWER:

5. ANSWER:

6. ANSWER:

7. Solve each inequality. Graph the solution set on a number line. ANSWER: 1. ANSWER:

8. ANSWER:

2. ANSWER: 9. ANSWER:

3. or ANSWER:

10. ANSWER: 4. or ANSWER:

11. MONEY Khalid is considering several types of paint for his bedroom. He estimates that he will need between 2 and 3 gallons. The table at the right shows 5. the price per gallon for each type of paint Khalid is ANSWER: considering. Write a compound inequality and determine how much he could be spending.

6. ANSWER:

ANSWER: between $43.96 and $77.94 7. Solve each inequality. Graph the solution set on ANSWER: a number line. 12. ANSWER:

8. ANSWER:

13. ANSWER:

9. ANSWER:

14. or ANSWER:

10. ANSWER:

15. or ANSWER:

11. MONEY Khalid is considering several types of paint for his bedroom. He estimates that he will need between 2 and 3 gallons. The table at the right shows the price per gallon for each type of paint Khalid is 16. considering. Write a compound inequality and determine how much he could be spending. ANSWER:

17. ANSWER:

1-6 SolvingANSWER: Compound and Absolute Value Inequalities between $43.96 and $77.94

Solve each inequality. Graph the solution set on 18. a number line. 12. ANSWER:

ANSWER:

19. 13. ANSWER: ANSWER:

14. or 20. ANSWER: ANSWER:

15. or 21. ANSWER: ANSWER:

16. ANSWER: 22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman

given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur 17. bone. ANSWER: b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value inequality that describes the woman’s height in centimeters. ANSWER: 18. a. ANSWER: b.

Write an absolute value inequality for each graph. eSolutions Manual - Powered by Cognero Page 2 23.

19. ANSWER:

ANSWER:

24. ANSWER:

20.

ANSWER: 25.

ANSWER:

26. 21. ANSWER: ANSWER:

27. ANSWER:

22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. 28. a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the ANSWER: height of a woman given the length of her femur bone. b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value 29. inequality that describes the woman’s height in ANSWER: centimeters. ANSWER: a. 30. b. ANSWER: Write an absolute value inequality for each graph. 31. DOGS The Labrador retriever is one of the most 23. recognized and popular dogs kept as a pet. Using the ANSWER: information given, write a compound inequality to describe the range of healthy weights for a fully grown female Labrador retriever.

24. ANSWER:

ANSWER: 25.

ANSWER: 32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is greater than the measure of either of its corresponding remote interior angles. Write two 26. inequalities to express the relationships among the

ANSWER: measures of the angles of ABC.

27. ANSWER: ANSWER:

28. Solve each inequality. Graph the solution set on ANSWER: a number line.

33. ANSWER:

29. ANSWER:

34. 30. ANSWER: ANSWER:

31. DOGS The Labrador retriever is one of the most 35. recognized and popular dogs kept as a pet. Using the information given, write a compound inequality to ANSWER: describe the range of healthy weights for a fully grown female Labrador retriever.

36. ANSWER:

ANSWER:

32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is 37. greater than the measure of either of its corresponding remote interior angles. Write two ANSWER: inequalities to express the relationships among the measures of the angles of ABC.

38. ANSWER:

ANSWER:

Solve each inequality. Graph the solution set on

a number line. 39. 33. ANSWER: ANSWER:

34. 40. ANSWER: ANSWER:

35. ANSWER: Write an algebraic expression to represent

each verbal expression. 41. numbers that are at least 4 units from –5 ANSWER: 36. ANSWER: 42. numbers that are no more than unit from 1

ANSWER:

37. ANSWER: 43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER:

39.

ANSWER:

a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write an absolute value inequality for templates with each 40. line color. b. Find the acceptable lengths for that part of a car if ANSWER: the template has each line color. c. Graph the solution set for each line color on a number line. d. The tolerance of which line color includes the tolerances of the other line colors? Explain your reasoning. Write an algebraic expression to represent each verbal expression. ANSWER: 41. numbers that are at least 4 units from –5 a. ANSWER:

42. numbers that are no more than unit from 1

c. ANSWER:

43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER:

d. Red; the red line color has the smallest tolerance, 44. AUTO RACING NASCAR rules stipulate that a , so the other line colors would be car must conform to a set of 32 templates, each well within their tolerances. shaped to fit a different contour of the car. When a template is placed on a car, the gap between it and Solve each inequality. Graph the solution set on the car cannot exceed the specified tolerance. Each a number line. template is marked on its edge with a colored line 45. that indicates the tolerance for the template. ANSWER:

46.

ANSWER: a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write an absolute value inequality for templates with each line color. b. Find the acceptable lengths for that part of a car if 47. the template has each line color. c. Graph the solution set for each line color on a ANSWER: number line. d. The tolerance of which line color includes the tolerances of the other line colors? Explain your reasoning. 48. ANSWER: a. ANSWER:

49. c. ANSWER:

50. ANSWER: d. Red; the red line color has the smallest tolerance, , so the other line colors would be well within their tolerances.

Solve each inequality. Graph the solution set on 51. HEALTH Hypoglycemia (low blood sugar) and a number line. hyperglycemia (high blood sugar) are potentially 45. dangerous and occur when a person’s blood sugar ANSWER: fluctuates by more than 38 mg from the normal blood sugar level of 88 mg. Write and solve an absolute

value inequality to describe blood sugar levels that are considered potentially dangerous. ANSWER:

46.

ANSWER: 52. AIR TRAVEL The airline on which Drew is flying has weight restrictions for checked baggage. Drew is checking one bag. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. 47. b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane? ANSWER:

48. ANSWER:

ANSWER: a. b. $25 49. ERROR ANALYSIS ANSWER: 53. David and Sarah are solving

. Is either of them correct? Explain your reasoning.

50.

ANSWER: ANSWER: Sample answer: David; when Sarah converted the absolute value into two inequalities, she mistakenly switched the inequality symbols. 51. HEALTH Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially 54. CHALLENGE Solve dangerous and occur when a person’s blood sugar fluctuates by more than 38 mg from the normal blood ANSWER: sugar level of 88 mg. Write and solve an absolute

value inequality to describe blood sugar levels that x < 0

are considered potentially dangerous. REASONING Determine whether each ANSWER: statement is true or false . If false, provide a counterexample. 55. The graph of a compound inequality involving an and statement is bounded on the left and right by two 52. AIR TRAVEL The airline on which Drew is flying values of x. has weight restrictions for checked baggage. Drew is checking one bag. ANSWER: a. Describe the range of weights that would classify False; sample answer: the graph of Drew’s bag as free, $25, $50, and unacceptable. x > 2 and x > 5 is a ray bounded only on one end. b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane? 56. The graph of a compound inequality involving an or statement contains a region of values that are not solutions. ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true. ANSWER: ANSWER: a. True b. $25 58. WRITING IN MATH An alternate definition of ERROR ANALYSIS 53. David and Sarah are solving absolute value is to define as the distance . Is either of them between a and b on the number line. Explain how correct? Explain your reasoning. this definition can be used to solve inequalities of the form .

ANSWER: Sample answer: represents the distance between some unknown value of the ANSWER: variable x and a point c on the number line. The solution set of the inequality is the set of all numbers Sample answer: David; when Sarah converted the such that the distance from the numbers to c is less absolute value into two inequalities, she mistakenly than r units. Use a number line to find the numbers switched that are r units from c in either direction. the inequality symbols. 59. REASONING The graphs of the solutions of two 54. CHALLENGE Solve different absolute value inequalities are shown. ANSWER: Compare and contrast the absolute value inequalities. x < 0

REASONING Determine whether each statement is true or false . If false, provide a counterexample. ANSWER: 55. The graph of a compound inequality involving an and Sample answer: The graph on the left indicates a statement is bounded on the left and right by two solution set from –3 to 5. The values of x. graph on the right indicates a solution ANSWER: set of all numbers less than or equal to –3 or greater than or equal to 5. False; sample answer: the graph of x > 2 and x > 5 is a ray bounded only on one end. 60. OPEN ENDED Write an absolute value inequality with a solution of 56. The graph of a compound inequality involving an or statement contains a region of values that are not ANSWER: solutions. Sample answer: ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line. 61. WHICH ONE DOESN’T BELONG? Identify the 57. The graph of a compound inequality involving an and compound inequality that is not the same as the other statement includes values that make all parts of the three. Explain your reasoning. given statement true.

ANSWER: True ANSWER: WRITING IN MATH 58. An alternate definition of Each of these has a non-empty solution set except absolute value is to define as the distance for x > 5 and x < 1. There are no values of x that are between a and b on the number line. Explain how simultaneously greater than 5 and less than 1. this definition can be used to solve inequalities of the form . 62. WRITING IN MATH Summarize the difference between and compound inequalities and or ANSWER: compound inequalities. Sample answer: represents ANSWER: the distance between some unknown value of the Sample answer: A compound inequality that contains variable x and a point c on the number line. The and is true if and only if both individual inequalities solution set of the inequality is the set of all numbers are true, while an inequality containing or only needs such that the distance from the numbers to c is less one of the individual inequalities to be true. than r units. Use a number line to find the numbers that are r units from c in either direction. 63. Which of the following best describes the graph of the equations below? 59. REASONING The graphs of the solutions of two different absolute value inequalities are shown. Compare and contrast the absolute value inequalities. A The lines have the same x-intercept. B The lines have the same y-intercept. C The lines are parallel. D The lines are perpendicular. ANSWER: ANSWER: Sample answer: The graph on the left indicates a C solution set from –3 to 5. The graph on the right indicates a solution 64. SAT/ACT Find an expression equivalent set of all numbers less than or equal to –3 or greater than or equal to 5. to

60. OPEN ENDED Write an absolute value inequality F with a solution of ANSWER: Sample answer: G

61. WHICH ONE DOESN’T BELONG? Identify the J compound inequality that is not the same as the other three. Explain your reasoning. K

ANSWER: ANSWER: Each of these has a non-empty solution set except K for x > 5 and x < 1. There are no values of x that are 65. GRIDDED RESPONSE How many cubes that simultaneously greater than 5 and less than 1. measure 4 centimeters on each side can be placed

62. WRITING IN MATH Summarize the difference completely inside the box below? between and compound inequalities and or compound inequalities. ANSWER: Sample answer: A compound inequality that contains and is true if and only if both individual inequalities are true, while an inequality containing or only needs ANSWER: one of the individual inequalities to be true. 60 63. Which of the following best describes the graph of 66. Which graph represents the solution set for the equations below?

A A The lines have the same x-intercept. B B The lines have the same y-intercept. C The lines are parallel. C D The lines are perpendicular. D ANSWER: C ANSWER: A 64. SAT/ACT Find an expression equivalent 67. HEALTH The National Heart Association recommends that less than 30% of a person’s total to daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old

F whose average caloric intake is between 2500 and 3300 Calories. a. Write an inequality that represents the suggested G fat intake for the person. b. What is the greatest suggested fat intake for the

H person? ANSWER:

J a. b.110g

K 68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. Her plane ticket is $375, and the hotel is $85 per night. ANSWER: a. Let f represent the cost of food for one day. Write K an inequality to represent this situation. b. Solve the inequality and interpret the solution. 65. GRIDDED RESPONSE How many cubes that measure 4 centimeters on each side can be placed ANSWER: completely inside the box below? a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER: ANSWER: 60

66. Which graph represents the solution set for 70.

ANSWER: A B

C 71. D ANSWER: ANSWER: A Name the property illustrated by each statement. 67. HEALTH The National Heart Association recommends that less than 30% of a person’s total 72. If then daily caloric intake come from fat. One gram of fat ANSWER: yields nine Calories. Consider a healthy 21-year-old Addition (=) whose average caloric intake is between 2500 and 3300 Calories. a. Write an inequality that represents the suggested 73. If and then fat intake for the person. b. What is the greatest suggested fat intake for the person? ANSWER: Transitive (=) ANSWER: a. 74. If then b.110g ANSWER: 68. TRAVEL Maggie is planning a 5-day trip to a family Assoc. (+) reunion. She wants to spend no more than $1000. Her plane ticket is $375, and the hotel is $85 per night. a. Let f represent the cost of food for one day. Write an inequality to represent this situation. b. Solve the inequality and interpret the solution. ANSWER: a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER:

70.

ANSWER:

71.

ANSWER:

Name the property illustrated by each statement. 72. If then ANSWER: Addition (=)

73. If and then

ANSWER: Transitive (=)

74. If then

ANSWER: Assoc. (+) Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

2. ANSWER:

3. or ANSWER:

4. or ANSWER:

5. ANSWER:

6. ANSWER:

7. ANSWER: Solve each inequality. Graph the solution set on a number line. 1. ANSWER: 8. ANSWER:

2. 9. ANSWER: ANSWER:

3. or ANSWER: 10.

ANSWER:

4. or ANSWER: 11. MONEY Khalid is considering several types of paint for his bedroom. He estimates that he will need between 2 and 3 gallons. The table at the right shows the price per gallon for each type of paint Khalid is considering. Write a compound inequality and 5. determine how much he could be spending. ANSWER:

ANSWER: ANSWER: between $43.96 and $77.94

Solve each inequality. Graph the solution set on 7. a number line. 12. ANSWER: ANSWER:

8. 13. ANSWER: ANSWER:

9. ANSWER: 14. or ANSWER:

10. ANSWER: 15. or ANSWER:

11. MONEY Khalid is considering several types of paint for his bedroom. He estimates that he will need 16. between 2 and 3 gallons. The table at the right shows the price per gallon for each type of paint Khalid is ANSWER: considering. Write a compound inequality and determine how much he could be spending.

17. ANSWER:

ANSWER: between $43.96 and $77.94 18.

Solve each inequality. Graph the solution set on ANSWER: a number line. 12. ANSWER:

19. ANSWER:

13. ANSWER:

20. ANSWER:

14. or ANSWER:

21.

15. or ANSWER:

ANSWER:

22. ANATOMY Forensic scientists use the equation h 16. = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. ANSWER: a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur bone. b. If the length of a female skeleton’s femur is 50 17. centimeters, write and solve an absolute value inequality that describes the woman’s height in ANSWER: centimeters.

ANSWER: a. b. 18. ANSWER: Write an absolute value inequality for each graph.

23. ANSWER:

19. ANSWER: 24.

ANSWER:

20. 25. ANSWER: ANSWER:

26. ANSWER: 21. ANSWER: 27. ANSWER:

22. ANATOMY Forensic scientists use the equation h 28. = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. ANSWER: a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur 29. bone. b. If the length of a female skeleton’s femur is 50 ANSWER: centimeters, write and solve an absolute value inequality that describes the woman’s height in centimeters. ANSWER: 30. a. ANSWER: 1-6 Solving Compound and Absolute Value Inequalities b.

Write an absolute value inequality for each 31. DOGS The Labrador retriever is one of the most graph. recognized and popular dogs kept as a pet. Using the information given, write a compound inequality to 23. describe the range of healthy weights for a fully ANSWER: grown female Labrador retriever.

24.

ANSWER: ANSWER:

25. 32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is ANSWER: greater than the measure of either of its corresponding remote interior angles. Write two inequalities to express the relationships among the measures of the angles of ABC. 26. ANSWER:

27. ANSWER: ANSWER:

Solve each inequality. Graph the solution set on a number line. 28. 33. ANSWER: ANSWER:

29. ANSWER: 34. ANSWER:

30. ANSWER: 35.

31. DOGS The Labrador retriever is one of the most ANSWER: recognized and popular dogs kept as a pet. Using the information given, write a compound inequality to eSolutionsdescribeManual the- Powered range ofby healthyCognero weights for a fully Page 3 grown female Labrador retriever. 36. ANSWER:

ANSWER:

37. 32. GEOMETRY The Exterior Angle Inequality ANSWER: Theorem states that an exterior angle measure is greater than the measure of either of its corresponding remote interior angles. Write two inequalities to express the relationships among the measures of the angles of ABC. 38. ANSWER:

ANSWER:

39. Solve each inequality. Graph the solution set on a number line. ANSWER: 33. ANSWER:

40. 34. ANSWER: ANSWER:

35. Write an algebraic expression to represent each verbal expression. ANSWER: 41. numbers that are at least 4 units from –5

ANSWER:

36. 42. numbers that are no more than unit from 1 ANSWER: ANSWER:

43. numbers that are at least 6 units but no more than 10 37. units from 2 ANSWER: ANSWER:

44. AUTO RACING NASCAR rules stipulate that a car must conform to a set of 32 templates, each

38. shaped to fit a different contour of the car. When a ANSWER: template is placed on a car, the gap between it and the car cannot exceed the specified tolerance. Each

template is marked on its edge with a colored line that indicates the tolerance for the template.

39.

ANSWER:

a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write an absolute value inequality for templates with each line color. b. Find the acceptable lengths for that part of a car if 40. the template has each line color. c. Graph the solution set for each line color on a ANSWER: number line. d. The tolerance of which line color includes the tolerances of the other line colors? Explain your reasoning. ANSWER: Write an algebraic expression to represent a. each verbal expression.

41. numbers that are at least 4 units from –5

ANSWER: b.

c. 42. numbers that are no more than unit from 1

ANSWER:

43. numbers that are at least 6 units but no more than 10 units from 2

ANSWER: d. Red; the red line color has the smallest tolerance, , so the other line colors would be well within their tolerances. 44. AUTO RACING NASCAR rules stipulate that a car must conform to a set of 32 templates, each Solve each inequality. Graph the solution set on shaped to fit a different contour of the car. When a a number line. template is placed on a car, the gap between it and 45. the car cannot exceed the specified tolerance. Each ANSWER: template is marked on its edge with a colored line

that indicates the tolerance for the template.

46. ANSWER:

a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write an absolute value inequality for templates with each 47. line color. b. Find the acceptable lengths for that part of a car if ANSWER: the template has each line color. c. Graph the solution set for each line color on a number line. d. The tolerance of which line color includes the tolerances of the other line colors? 48. Explain your reasoning. ANSWER: ANSWER: a.

b. 49.

ANSWER:

50. ANSWER:

d. Red; the red line color has the smallest tolerance, , so the other line colors would be well within their tolerances. 51. HEALTH Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially Solve each inequality. Graph the solution set on dangerous and occur when a person’s blood sugar a number line. fluctuates by more than 38 mg from the normal blood 45. sugar level of 88 mg. Write and solve an absolute value inequality to describe blood sugar levels that ANSWER: are considered potentially dangerous.

ANSWER:

46. 52. AIR TRAVEL The airline on which Drew is flying has weight restrictions for checked baggage. Drew is ANSWER: checking one bag. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane? 47. ANSWER:

48. ANSWER: ANSWER: a. b. $25

53. ERROR ANALYSIS David and Sarah are solving 49. . Is either of them ANSWER: correct? Explain your reasoning.

50. ANSWER: ANSWER: Sample answer: David; when Sarah converted the absolute value into two inequalities, she mistakenly switched the inequality symbols.

52. AIR TRAVEL The airline on which Drew is flying ANSWER: has weight restrictions for checked baggage. Drew is False; sample answer: the graph of checking one bag. x > 2 and x > 5 is a ray bounded only on one end. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. 56. The graph of a compound inequality involving an or b. If Drew’s bag weighs 68 pounds, how much will statement contains a region of values that are not he pay to take it on the plane? solutions.

ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true. ANSWER: ANSWER: True a. 58. WRITING IN MATH An alternate definition of b. $25 absolute value is to define as the distance between a and b on the number line. Explain how 53. ERROR ANALYSIS David and Sarah are solving this definition can be used to solve inequalities of the . Is either of them form . correct? Explain your reasoning. ANSWER: Sample answer: represents the distance between some unknown value of the variable x and a point c on the number line. The solution set of the inequality is the set of all numbers such that the distance from the numbers to c is less ANSWER: than r units. Use a number line to find the numbers Sample answer: David; when Sarah converted the that are r units from c in either direction. absolute value into two inequalities, she mistakenly switched 59. REASONING The graphs of the solutions of two the inequality symbols. different absolute value inequalities are shown. Compare and contrast the absolute value inequalities. 54. CHALLENGE Solve

ANSWER: 60. OPEN ENDED Write an absolute value inequality False; sample answer: the graph of with a solution of x > 2 and x > 5 is a ray bounded only on one end. ANSWER: 56. The graph of a compound inequality involving an or Sample answer: statement contains a region of values that are not solutions. ANSWER: 61. WHICH ONE DOESN’T BELONG? Identify the False; sample answer: the graph of compound inequality that is not the same as the other x > 2 or x < 3 includes the entire number line. three. Explain your reasoning. 57. The graph of a compound inequality involving an and

statement includes values that make all parts of the given statement true. ANSWER: ANSWER: True Each of these has a non-empty solution set except for x > 5 and x < 1. There are no values of x that are 58. WRITING IN MATH An alternate definition of simultaneously greater than 5 and less than 1. absolute value is to define as the distance between a and b on the number line. Explain how 62. WRITING IN MATH Summarize the difference this definition can be used to solve inequalities of the between and compound inequalities and or

form . compound inequalities. ANSWER: ANSWER: Sample answer: A compound inequality that contains Sample answer: represents and is true if and only if both individual inequalities the distance between some unknown value of the are true, while an inequality containing or only needs variable x and a point c on the number line. The one of the individual inequalities to be true. solution set of the inequality is the set of all numbers such that the distance from the numbers to c is less 63. Which of the following best describes the graph of than r units. Use a number line to find the numbers the equations below? that are r units from c in either direction.

59. REASONING The graphs of the solutions of two A The lines have the same x-intercept. different absolute value inequalities are shown. B The lines have the same y-intercept. Compare and contrast the absolute value inequalities. C The lines are parallel. D The lines are perpendicular.

ANSWER: C ANSWER: SAT/ACT Sample answer: The graph on the left indicates a 64. Find an expression equivalent solution set from –3 to 5. The graph on the right indicates a solution to set of all numbers less than or equal to –3 or greater than or equal to 5. F 60. OPEN ENDED Write an absolute value inequality

with a solution of G ANSWER: Sample answer: H

61. WHICH ONE DOESN’T BELONG? Identify the compound inequality that is not the same as the other K three. Explain your reasoning.

ANSWER: K ANSWER: 65. GRIDDED RESPONSE How many cubes that Each of these has a non-empty solution set except measure 4 centimeters on each side can be placed for x > 5 and x < 1. There are no values of x that are completely inside the box below? simultaneously greater than 5 and less than 1.

62. WRITING IN MATH Summarize the difference between and compound inequalities and or compound inequalities.

ANSWER: Sample answer: A compound inequality that contains ANSWER: and is true if and only if both individual inequalities 60 are true, while an inequality containing or only needs one of the individual inequalities to be true. 66. Which graph represents the solution set for

63. Which of the following best describes the graph of the equations below? A

A The lines have the same x-intercept. C B The lines have the same y-intercept. C The lines are parallel. D D The lines are perpendicular. ANSWER: ANSWER: A C 67. HEALTH The National Heart Association 64. SAT/ACT Find an expression equivalent recommends that less than 30% of a person’s total daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old to whose average caloric intake is between 2500 and 3300 Calories. a. Write an inequality that represents the suggested F fat intake for the person. b. What is the greatest suggested fat intake for the G person? ANSWER:

H a. b.110g

J 68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. K Her plane ticket is $375, and the hotel is $85 per night. a. Let f represent the cost of food for one day. Write an inequality to represent this situation. ANSWER: b. Solve the inequality and interpret the solution. K ANSWER: 65. GRIDDED RESPONSE How many cubes that a. measure 4 centimeters on each side can be placed b. She can spend no more than $40 per day on food. completely inside the box below? Solve each equation. Check your solutions. 69.

ANSWER:

ANSWER: 60 70.

66. Which graph represents the solution set for ANSWER:

B 71.

C ANSWER:

D Name the property illustrated by each ANSWER: statement. A 72. If then 67. HEALTH The National Heart Association ANSWER: recommends that less than 30% of a person’s total Addition (=) daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old whose average caloric intake is between 2500 and 73. If and then 3300 Calories. a. Write an inequality that represents the suggested ANSWER: fat intake for the person. b. What is the greatest suggested fat intake for the Transitive (=) person? 74. If then ANSWER: a. ANSWER: b.110g Assoc. (+)

68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. Her plane ticket is $375, and the hotel is $85 per night. a. Let f represent the cost of food for one day. Write an inequality to represent this situation. b. Solve the inequality and interpret the solution. ANSWER: a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER:

70.

ANSWER:

71.

ANSWER:

Name the property illustrated by each statement. 72. If then ANSWER: Addition (=)

73. If and then

ANSWER: Transitive (=)

74. If then

ANSWER: Assoc. (+) Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

2. ANSWER:

3. or ANSWER:

4. or ANSWER:

5. ANSWER:

6. ANSWER:

7. ANSWER: Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

8. ANSWER:

2. 9. ANSWER: ANSWER:

3. or ANSWER: 10.

ANSWER:

ANSWER: ANSWER:

between $43.96 and $77.94

Solve each inequality. Graph the solution set on a number line. 7. 12. ANSWER: ANSWER:

8. 13. ANSWER: ANSWER:

9. ANSWER: 14. or ANSWER:

10. 15. or ANSWER: ANSWER:

17. ANSWER:

ANSWER: 18. between $43.96 and $77.94 ANSWER: Solve each inequality. Graph the solution set on

a number line. 12. ANSWER:

19. ANSWER:

13. ANSWER:

20. ANSWER: 14. or ANSWER:

21. ANSWER:

15. or ANSWER:

ANSWER: a. b. 18. Write an absolute value inequality for each ANSWER: graph.

23. ANSWER:

19.

ANSWER: 24.

ANSWER:

25. 20. ANSWER: ANSWER:

26. ANSWER:

21. ANSWER: 27. ANSWER:

22. ANATOMY Forensic scientists use the equation h 28. = 2.6f + 47.2 to estimate the height h of a woman ANSWER:

given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur 29. bone. b. If the length of a female skeleton’s femur is 50 ANSWER: centimeters, write and solve an absolute value inequality that describes the woman’s height in centimeters. 30. ANSWER: a. ANSWER: b.

24.

ANSWER: ANSWER:

32. GEOMETRY The Exterior Angle Inequality 25. Theorem states that an exterior angle measure is ANSWER: greater than the measure of either of its corresponding remote interior angles. Write two inequalities to express the relationships among the measures of the angles of ABC. 26. ANSWER:

27. ANSWER: ANSWER:

Solve each inequality. Graph the solution set on a number line. 28. 33. ANSWER: ANSWER:

29. ANSWER: 34.

ANSWER:

30. ANSWER: 35. ANSWER: 31. DOGS The Labrador retriever is one of the most recognized and popular dogs kept as a pet. Using the information given, write a compound inequality to describe the range of healthy weights for a fully grown female Labrador retriever. 36. ANSWER:

ANSWER:

39. Solve each inequality. Graph the solution set on a number line. ANSWER: 33. ANSWER:

40.

34. ANSWER: ANSWER:

1-6 Solving Compound and Absolute Value Inequalities

35. Write an algebraic expression to represent each verbal expression. ANSWER: 41. numbers that are at least 4 units from –5

ANSWER:

36. 42. numbers that are no more than unit from 1 ANSWER: ANSWER:

43. numbers that are at least 6 units but no more than 10 37. units from 2 ANSWER: ANSWER:

44. AUTO RACING NASCAR rules stipulate that a car must conform to a set of 32 templates, each 38. shaped to fit a different contour of the car. When a template is placed on a car, the gap between it and ANSWER: the car cannot exceed the specified tolerance. Each template is marked on its edge with a colored line that indicates the tolerance for the template.

39.

ANSWER:

c. 42. numbers that are no more than unit from 1

ANSWER:

43. numbers that are at least 6 units but no more than 10

units from 2 ANSWER: d. Red; the red line color has the smallest tolerance, , so the other line colors would be well within their tolerances.

44. AUTO RACING NASCAR rules stipulate that a Solve each inequality. Graph the solution set on car must conform to a set of 32 templates, each a number line. shaped to fit a different contour of the car. When a 45. template is placed on a car, the gap between it and the car cannot exceed the specified tolerance. Each ANSWER: template is marked on its edge with a colored line that indicates the tolerance for the template.

46. ANSWER:

a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write an absolute value inequality for templates with each 47. line color. ANSWER: b. Find the acceptable lengths for that part of a car if the template has each line color. c. Graph the solution set for each line color on a number line. d. The tolerance of which line color includes the 48. tolerances of the other line colors? Explain your reasoning. ANSWER: ANSWER: a.

b. 49. ANSWER:

50. ANSWER:

ANSWER:

52. AIR TRAVEL The airline on which Drew is flying 46. has weight restrictions for checked baggage. Drew is ANSWER: checking one bag. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane? 47. ANSWER:

48.

ANSWER: ANSWER: a. b. $25

53. ERROR ANALYSIS David and Sarah are solving 49. . Is either of them correct? Explain your reasoning. ANSWER:

50. ANSWER: Sample answer: David; when Sarah converted the ANSWER: absolute value into two inequalities, she mistakenly switched the inequality symbols.

54. CHALLENGE Solve 51. HEALTH Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially ANSWER: dangerous and occur when a person’s blood sugar x < 0 fluctuates by more than 38 mg from the normal blood sugar level of 88 mg. Write and solve an absolute REASONING Determine whether each value inequality to describe blood sugar levels that statement is true or false . If false, provide a are considered potentially dangerous. counterexample. 55. The graph of a compound inequality involving an and ANSWER: statement is bounded on the left and right by two values of x. ANSWER: AIR TRAVEL 52. The airline on which Drew is flying False; sample answer: the graph of has weight restrictions for checked baggage. Drew is x > 2 and x > 5 is a ray bounded only on one end. checking one bag. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. 56. The graph of a compound inequality involving an or b. If Drew’s bag weighs 68 pounds, how much will statement contains a region of values that are not he pay to take it on the plane? solutions. ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true. ANSWER:

True ANSWER: a. 58. WRITING IN MATH An alternate definition of b. $25 absolute value is to define as the distance between a and b on the number line. Explain how 53. ERROR ANALYSIS David and Sarah are solving this definition can be used to solve inequalities of the . Is either of them form . correct? Explain your reasoning. ANSWER: Sample answer: represents the distance between some unknown value of the variable x and a point c on the number line. The solution set of the inequality is the set of all numbers such that the distance from the numbers to c is less ANSWER: than r units. Use a number line to find the numbers Sample answer: David; when Sarah converted the that are r units from c in either direction. absolute value into two inequalities, she mistakenly switched 59. REASONING The graphs of the solutions of two the inequality symbols. different absolute value inequalities are shown. Compare and contrast the absolute value inequalities. 54. CHALLENGE Solve

ANSWER: x < 0 REASONING Determine whether each ANSWER: statement is true or false . If false, provide a Sample answer: The graph on the left indicates a counterexample. solution set from –3 to 5. The 55. The graph of a compound inequality involving an and graph on the right indicates a solution statement is bounded on the left and right by two set of all numbers less than or equal to values of x. –3 or greater than or equal to 5. ANSWER: 60. OPEN ENDED Write an absolute value inequality False; sample answer: the graph of with a solution of x > 2 and x > 5 is a ray bounded only on one end. ANSWER: Sample answer: 56. The graph of a compound inequality involving an or statement contains a region of values that are not solutions.

ANSWER: 61. WHICH ONE DOESN’T BELONG? Identify the False; sample answer: the graph of compound inequality that is not the same as the other x > 2 or x < 3 includes the entire number line. three. Explain your reasoning.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true. ANSWER: ANSWER: True Each of these has a non-empty solution set except for x > 5 and x < 1. There are no values of x that are 58. WRITING IN MATH An alternate definition of simultaneously greater than 5 and less than 1. absolute value is to define as the distance 62. WRITING IN MATH Summarize the difference between a and b on the number line. Explain how between and compound inequalities and or this definition can be used to solve inequalities of the compound inequalities. form . ANSWER: ANSWER: Sample answer: A compound inequality that contains Sample answer: represents and is true if and only if both individual inequalities the distance between some unknown value of the are true, while an inequality containing or only needs

variable x and a point c on the number line. The one of the individual inequalities to be true. solution set of the inequality is the set of all numbers 63. Which of the following best describes the graph of such that the distance from the numbers to c is less the equations below? than r units. Use a number line to find the numbers that are r units from c in either direction.

ANSWER: 64. SAT/ACT Find an expression equivalent Sample answer: The graph on the left indicates a solution set from –3 to 5. The to graph on the right indicates a solution set of all numbers less than or equal to

–3 or greater than or equal to 5. F

60. OPEN ENDED Write an absolute value inequality with a solution of G ANSWER: Sample answer: H

61. WHICH ONE DOESN’T BELONG? Identify the compound inequality that is not the same as the other K three. Explain your reasoning.

62. WRITING IN MATH Summarize the difference between and compound inequalities and or compound inequalities.

ANSWER: ANSWER: Sample answer: A compound inequality that contains 60 and is true if and only if both individual inequalities are true, while an inequality containing or only needs 66. Which graph represents the solution set for one of the individual inequalities to be true. 63. Which of the following best describes the graph of the equations below? A B

A The lines have the same x-intercept. C B The lines have the same y-intercept. D C The lines are parallel. D The lines are perpendicular. ANSWER: A ANSWER: C 67. HEALTH The National Heart Association recommends that less than 30% of a person’s total 64. SAT/ACT Find an expression equivalent daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old to whose average caloric intake is between 2500 and 3300 Calories. a. Write an inequality that represents the suggested F fat intake for the person. b. What is the greatest suggested fat intake for the person? G ANSWER: H a. b.110g

an inequality to represent this situation. ANSWER: b. Solve the inequality and interpret the solution. K ANSWER: 65. GRIDDED RESPONSE How many cubes that a. measure 4 centimeters on each side can be placed b. She can spend no more than $40 per day on food. completely inside the box below? Solve each equation. Check your solutions. 69.

ANSWER:

ANSWER: 60 70. 66. Which graph represents the solution set for ANSWER:

A 71. B ANSWER: C D Name the property illustrated by each ANSWER: statement. A 72. If then

67. HEALTH The National Heart Association ANSWER: recommends that less than 30% of a person’s total Addition (=) daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old 73. If and then whose average caloric intake is between 2500 and 3300 Calories. a. Write an inequality that represents the suggested ANSWER: fat intake for the person. Transitive (=) b. What is the greatest suggested fat intake for the

person? 74. If then ANSWER: ANSWER: a. Assoc. (+) b.110g

Solve each equation. Check your solutions. 69.

ANSWER:

70.

ANSWER:

71.

ANSWER:

Name the property illustrated by each statement. 72. If then ANSWER: Addition (=)

73. If and then

ANSWER: Transitive (=)

74. If then

ANSWER: Assoc. (+) Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

2. ANSWER:

3. or ANSWER:

4. or ANSWER:

5. ANSWER:

6. ANSWER:

7. ANSWER:

Solve each inequality. Graph the solution set on a number line. 1.

ANSWER: 8.

ANSWER:

2. 9. ANSWER: ANSWER:

3. or ANSWER: 10. ANSWER:

5. determine how much he could be spending.

ANSWER:

6. ANSWER: ANSWER: between $43.96 and $77.94

Solve each inequality. Graph the solution set on a number line. 7. 12. ANSWER: ANSWER:

8. 13. ANSWER: ANSWER:

9. 14. or ANSWER: ANSWER:

10. 15. or ANSWER: ANSWER:

11. MONEY Khalid is considering several types of paint 16. for his bedroom. He estimates that he will need between 2 and 3 gallons. The table at the right shows ANSWER: the price per gallon for each type of paint Khalid is considering. Write a compound inequality and determine how much he could be spending.

17. ANSWER:

ANSWER: 18. between $43.96 and $77.94 ANSWER: Solve each inequality. Graph the solution set on a number line. 12. ANSWER:

19. ANSWER:

13. ANSWER:

20. ANSWER: 14. or ANSWER:

21. ANSWER: 15. or ANSWER:

22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman 16. given the length in centimeters f of her femur bone. ANSWER: a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur bone. b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value

17. inequality that describes the woman’s height in ANSWER: centimeters. ANSWER: a. b. 18. Write an absolute value inequality for each ANSWER: graph.

23. ANSWER:

19. ANSWER: 24. ANSWER:

25. 20. ANSWER: ANSWER:

26. ANSWER:

21. ANSWER: 27.

ANSWER:

28. 22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman ANSWER: given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur 29. bone. ANSWER: b . If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value inequality that describes the woman’s height in centimeters. 30. ANSWER: ANSWER: a.

b. 31. DOGS The Labrador retriever is one of the most Write an absolute value inequality for each recognized and popular dogs kept as a pet. Using the graph. information given, write a compound inequality to 23. describe the range of healthy weights for a fully grown female Labrador retriever. ANSWER:

24. ANSWER: ANSWER:

32. GEOMETRY The Exterior Angle Inequality 25. Theorem states that an exterior angle measure is greater than the measure of either of its ANSWER: corresponding remote interior angles. Write two inequalities to express the relationships among the measures of the angles of ABC. 26. ANSWER:

27. ANSWER: ANSWER: Solve each inequality. Graph the solution set on a number line. 33. 28. ANSWER: ANSWER:

29. ANSWER: 34.

ANSWER:

ANSWER: 37.

32. GEOMETRY The Exterior Angle Inequality ANSWER: Theorem states that an exterior angle measure is greater than the measure of either of its corresponding remote interior angles. Write two inequalities to express the relationships among the measures of the angles of ABC. 38. ANSWER:

ANSWER:

39. Solve each inequality. Graph the solution set on ANSWER: a number line. 33. ANSWER:

40.

34. ANSWER:

ANSWER:

Write an algebraic expression to represent 35. each verbal expression. ANSWER: 41. numbers that are at least 4 units from –5 ANSWER:

36. 42. numbers that are no more than unit from 1 ANSWER: ANSWER:

43. numbers that are at least 6 units but no more than 10 37. units from 2 ANSWER: ANSWER:

39.

ANSWER:

40. the template has each line color. c. Graph the solution set for each line color on a

ANSWER: number line. d. The tolerance of which line color includes the

tolerances of the other line colors? Explain your reasoning. ANSWER: a. Write an algebraic expression to represent each verbal expression. 41. numbers that are at least 4 units from –5 ANSWER: b.

c. 42. numbers that are no more than unit from 1

ANSWER:

43. numbers that are at least 6 units but no more than 10 units from 2 d. Red; the red line color has the smallest tolerance, ANSWER: 1-6 Solving Compound and Absolute Value Inequalities , so the other line colors would be well within their tolerances.

46. ANSWER:

a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write 47. an absolute value inequality for templates with each line color. ANSWER: b. Find the acceptable lengths for that part of a car if the template has each line color. c. Graph the solution set for each line color on a number line. d. The tolerance of which line color includes the 48. tolerances of the other line colors? Explain your reasoning. ANSWER:

ANSWER: a.

49. b. ANSWER:

50. ANSWER:

d. Red; the red line color has the smallest tolerance, , so the other line colors would be 51. HEALTH Hypoglycemia (low blood sugar) and well within their tolerances. hyperglycemia (high blood sugar) are potentially dangerous and occur when a person’s blood sugar Solve each inequality. Graph the solution set on fluctuates by more than 38 mg from the normal blood a number line. sugar level of 88 mg. Write and solve an absolute 45. eSolutions Manual - Powered by Cognero value inequality to describe blood sugar levels thatPage 5 ANSWER: are considered potentially dangerous. ANSWER:

52. AIR TRAVEL The airline on which Drew is flying 46. has weight restrictions for checked baggage. Drew is checking one bag. ANSWER: a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane?

47. ANSWER:

48.

ANSWER: ANSWER: a. b. $25

53. ERROR ANALYSIS David and Sarah are solving . Is either of them 49. correct? Explain your reasoning. ANSWER:

ANSWER: 50. Sample answer: David; when Sarah converted the ANSWER: absolute value into two inequalities, she mistakenly switched the inequality symbols.

54. CHALLENGE Solve

51. HEALTH Hypoglycemia (low blood sugar) and ANSWER: hyperglycemia (high blood sugar) are potentially dangerous and occur when a person’s blood sugar x < 0 fluctuates by more than 38 mg from the normal blood REASONING Determine whether each sugar level of 88 mg. Write and solve an absolute statement is true or false . If false, provide a value inequality to describe blood sugar levels that counterexample. are considered potentially dangerous. 55. The graph of a compound inequality involving an and ANSWER: statement is bounded on the left and right by two values of x. ANSWER: 52. AIR TRAVEL The airline on which Drew is flying False; sample answer: the graph of has weight restrictions for checked baggage. Drew is x > 2 and x > 5 is a ray bounded only on one end. checking one bag. a. Describe the range of weights that would classify 56. The graph of a compound inequality involving an or

Drew’s bag as free, $25, $50, and unacceptable. statement contains a region of values that are not b. If Drew’s bag weighs 68 pounds, how much will solutions. he pay to take it on the plane? ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true. ANSWER: True ANSWER: 58. WRITING IN MATH An alternate definition of a. absolute value is to define as the distance b. $25 between a and b on the number line. Explain how 53. ERROR ANALYSIS David and Sarah are solving this definition can be used to solve inequalities of the . Is either of them form . correct? Explain your reasoning. ANSWER: Sample answer: represents the distance between some unknown value of the variable x and a point c on the number line. The solution set of the inequality is the set of all numbers such that the distance from the numbers to c is less ANSWER: than r units. Use a number line to find the numbers

Sample answer: David; when Sarah converted the that are r units from c in either direction. absolute value into two inequalities, she mistakenly 59. REASONING The graphs of the solutions of two switched different absolute value inequalities are shown. the inequality symbols. Compare and contrast the absolute value inequalities. 54. CHALLENGE Solve

ANSWER: x < 0 ANSWER: REASONING Determine whether each Sample answer: The graph on the left indicates a statement is true or false . If false, provide a solution set from –3 to 5. The counterexample. graph on the right indicates a solution 55. The graph of a compound inequality involving an and set of all numbers less than or equal to statement is bounded on the left and right by two –3 or greater than or equal to 5. values of x. ANSWER: 60. OPEN ENDED Write an absolute value inequality False; sample answer: the graph of with a solution of x > 2 and x > 5 is a ray bounded only on one end. ANSWER: Sample answer: 56. The graph of a compound inequality involving an or statement contains a region of values that are not solutions. ANSWER: 61. WHICH ONE DOESN’T BELONG? Identify the False; sample answer: the graph of compound inequality that is not the same as the other three. Explain your reasoning. x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true. ANSWER: ANSWER: Each of these has a non-empty solution set except True for x > 5 and x < 1. There are no values of x that are simultaneously greater than 5 and less than 1. 58. WRITING IN MATH An alternate definition of absolute value is to define as the distance 62. WRITING IN MATH Summarize the difference between a and b on the number line. Explain how between and compound inequalities and or this definition can be used to solve inequalities of the compound inequalities.

form . ANSWER: ANSWER: Sample answer: A compound inequality that contains and is true if and only if both individual inequalities Sample answer: represents are true, while an inequality containing or only needs the distance between some unknown value of the one of the individual inequalities to be true. variable x and a point c on the number line. The solution set of the inequality is the set of all numbers 63. Which of the following best describes the graph of such that the distance from the numbers to c is less the equations below? than r units. Use a number line to find the numbers that are r units from c in either direction. A 59. REASONING The graphs of the solutions of two The lines have the same x-intercept. different absolute value inequalities are shown. B The lines have the same y-intercept. Compare and contrast the absolute value inequalities. C The lines are parallel. D The lines are perpendicular.

ANSWER: C

60. OPEN ENDED Write an absolute value inequality G with a solution of

ANSWER: H Sample answer:

61. WHICH ONE DOESN’T BELONG? Identify the K compound inequality that is not the same as the other three. Explain your reasoning. ANSWER: K

ANSWER: 65. GRIDDED RESPONSE How many cubes that Each of these has a non-empty solution set except measure 4 centimeters on each side can be placed

for x > 5 and x < 1. There are no values of x that are completely inside the box below? simultaneously greater than 5 and less than 1.

62. WRITING IN MATH Summarize the difference between and compound inequalities and or compound inequalities. ANSWER: ANSWER: Sample answer: A compound inequality that contains 60 and is true if and only if both individual inequalities are true, while an inequality containing or only needs 66. Which graph represents the solution set for one of the individual inequalities to be true.

63. Which of the following best describes the graph of A the equations below? B

A The lines have the same x-intercept. C B The lines have the same y-intercept. D C The lines are parallel. ANSWER: D The lines are perpendicular. A ANSWER: C 67. HEALTH The National Heart Association recommends that less than 30% of a person’s total 64. SAT/ACT Find an expression equivalent daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old to whose average caloric intake is between 2500 and 3300 Calories. a. Write an inequality that represents the suggested F fat intake for the person. b. What is the greatest suggested fat intake for the person? G ANSWER: a. H b.110g

J 68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. Her plane ticket is $375, and the hotel is $85 per K night. a. Let f represent the cost of food for one day. Write an inequality to represent this situation. b. Solve the inequality and interpret the solution. ANSWER: K ANSWER: a. 65. GRIDDED RESPONSE How many cubes that b. She can spend no more than $40 per day on food. measure 4 centimeters on each side can be placed completely inside the box below? Solve each equation. Check your solutions. 69.

ANSWER:

ANSWER: 70. 60 ANSWER: 66. Which graph represents the solution set for

A 71. B ANSWER: C

D Name the property illustrated by each ANSWER: statement. A 72. If then ANSWER: 67. HEALTH The National Heart Association Addition (=) recommends that less than 30% of a person’s total daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old 73. If and then whose average caloric intake is between 2500 and 3300 Calories. a. Write an inequality that represents the suggested ANSWER: fat intake for the person. Transitive (=) b. What is the greatest suggested fat intake for the person? 74. If then

ANSWER: ANSWER: a. Assoc. (+) b.110g

Solve each equation. Check your solutions. 69.

ANSWER:

70.

ANSWER:

71.

ANSWER:

Name the property illustrated by each statement. 72. If then ANSWER: Addition (=)

73. If and then

ANSWER: Transitive (=)

74. If then

ANSWER: Assoc. (+) Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

2. ANSWER:

3. or ANSWER:

4. or ANSWER:

5. ANSWER:

6. ANSWER:

Solve each inequality. Graph the solution set on ANSWER: a number line. 1. ANSWER:

8. ANSWER:

2. ANSWER: 9. ANSWER:

3. or ANSWER: 10. ANSWER:

4. or ANSWER:

11. MONEY Khalid is considering several types of paint for his bedroom. He estimates that he will need between 2 and 3 gallons. The table at the right shows the price per gallon for each type of paint Khalid is 5. considering. Write a compound inequality and determine how much he could be spending. ANSWER:

ANSWER:

ANSWER: between $43.96 and $77.94

Solve each inequality. Graph the solution set on 7. a number line. ANSWER: 12. ANSWER:

ANSWER: 13.

ANSWER:

9. ANSWER:

14. or ANSWER:

10.

ANSWER: 15. or

ANSWER:

11. MONEY Khalid is considering several types of paint for his bedroom. He estimates that he will need between 2 and 3 gallons. The table at the right shows 16. the price per gallon for each type of paint Khalid is considering. Write a compound inequality and ANSWER: determine how much he could be spending.

17. ANSWER:

ANSWER: between $43.96 and $77.94 18. Solve each inequality. Graph the solution set on ANSWER: a number line.

12. ANSWER:

19. ANSWER: 13. ANSWER:

20. 14. or ANSWER: ANSWER:

21. 15. or ANSWER: ANSWER:

16. 22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman ANSWER: given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur bone. 17. b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value ANSWER: inequality that describes the woman’s height in centimeters. ANSWER: a. 18. b. ANSWER: Write an absolute value inequality for each graph. 23. ANSWER:

19. ANSWER: 24. ANSWER:

20. 25. ANSWER: ANSWER:

26. ANSWER: 21.

ANSWER:

27. ANSWER:

22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman 28. given the length in centimeters f of her femur bone. ANSWER: a . Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur bone. 29. b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value ANSWER: inequality that describes the woman’s height in centimeters. ANSWER: 30. a. ANSWER: b.

Write an absolute value inequality for each graph. 31. DOGS The Labrador retriever is one of the most recognized and popular dogs kept as a pet. Using the 23. information given, write a compound inequality to describe the range of healthy weights for a fully ANSWER: grown female Labrador retriever.

24. ANSWER: ANSWER:

25. 32. GEOMETRY The Exterior Angle Inequality ANSWER: Theorem states that an exterior angle measure is greater than the measure of either of its corresponding remote interior angles. Write two inequalities to express the relationships among the 26. measures of the angles of ABC. ANSWER:

27. ANSWER: ANSWER:

Solve each inequality. Graph the solution set on 28. a number line. 33. ANSWER: ANSWER:

29. ANSWER: 34. ANSWER: 30. ANSWER:

35. 31. DOGS The Labrador retriever is one of the most ANSWER: recognized and popular dogs kept as a pet. Using the information given, write a compound inequality to describe the range of healthy weights for a fully grown female Labrador retriever.

36. ANSWER:

ANSWER:

32. GEOMETRY The Exterior Angle Inequality 37. Theorem states that an exterior angle measure is ANSWER: greater than the measure of either of its

corresponding remote interior angles. Write two inequalities to express the relationships among the measures of the angles of ABC. 38. ANSWER:

ANSWER:

Solve each inequality. Graph the solution set on 39. a number line. 33. ANSWER:

ANSWER:

40. 34. ANSWER: ANSWER:

35. Write an algebraic expression to represent ANSWER: each verbal expression. 41. numbers that are at least 4 units from –5 ANSWER:

36.

ANSWER: 42. numbers that are no more than unit from 1

ANSWER:

37. 43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER: ANSWER:

44. AUTO RACING NASCAR rules stipulate that a 38. car must conform to a set of 32 templates, each shaped to fit a different contour of the car. When a ANSWER: template is placed on a car, the gap between it and the car cannot exceed the specified tolerance. Each template is marked on its edge with a colored line that indicates the tolerance for the template.

39.

ANSWER:

a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write an absolute value inequality for templates with each line color. 40. b. Find the acceptable lengths for that part of a car if the template has each line color. ANSWER: c. Graph the solution set for each line color on a number line. d. The tolerance of which line color includes the tolerances of the other line colors? Explain your reasoning. ANSWER: Write an algebraic expression to represent each verbal expression. a. 41. numbers that are at least 4 units from –5 ANSWER: b.

42. numbers that are no more than unit from 1 c.

ANSWER:

43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER: d. Red; the red line color has the smallest tolerance, , so the other line colors would be well within their tolerances. 44. AUTO RACING NASCAR rules stipulate that a car must conform to a set of 32 templates, each Solve each inequality. Graph the solution set on shaped to fit a different contour of the car. When a a number line. template is placed on a car, the gap between it and 45. the car cannot exceed the specified tolerance. Each template is marked on its edge with a colored line ANSWER: that indicates the tolerance for the template.

46.

ANSWER:

a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write an absolute value inequality for templates with each line color. 47. b. Find the acceptable lengths for that part of a car if ANSWER: the template has each line color. c. Graph the solution set for each line color on a number line. d. The tolerance of which line color includes the tolerances of the other line colors?

Explain your reasoning. 48. ANSWER: ANSWER: a.

49. ANSWER: c.

50. ANSWER:

d. Red; the red line color has the smallest tolerance, , so the other line colors would be well within their tolerances. 51. HEALTH Hypoglycemia (low blood sugar) and Solve each inequality. Graph the solution set on hyperglycemia (high blood sugar) are potentially a number line. dangerous and occur when a person’s blood sugar 45. fluctuates by more than 38 mg from the normal blood sugar level of 88 mg. Write and solve an absolute ANSWER: value inequality to describe blood sugar levels that are considered potentially dangerous. ANSWER:

46. 52. AIR TRAVEL The airline on which Drew is flying ANSWER: has weight restrictions for checked baggage. Drew is

checking one bag. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. b. If Drew’s bag weighs 68 pounds, how much will 47. he pay to take it on the plane?

ANSWER:

48. ANSWER:

ANSWER: a. b. $25

49. 53. ERROR ANALYSIS David and Sarah are solving . Is either of them ANSWER: correct? Explain your reasoning.

50. ANSWER: ANSWER: Sample answer: David; when Sarah converted the absolute value into two inequalities, she mistakenly 1-6 Solving Compound and Absolute Value Inequalities switched the inequality symbols.

51. HEALTH Hypoglycemia (low blood sugar) and 54. CHALLENGE Solve hyperglycemia (high blood sugar) are potentially dangerous and occur when a person’s blood sugar ANSWER: fluctuates by more than 38 mg from the normal blood x < 0 sugar level of 88 mg. Write and solve an absolute value inequality to describe blood sugar levels that REASONING Determine whether each are considered potentially dangerous. statement is true or false . If false, provide a counterexample. ANSWER: 55. The graph of a compound inequality involving an and statement is bounded on the left and right by two values of x. 52. AIR TRAVEL The airline on which Drew is flying ANSWER: has weight restrictions for checked baggage. Drew is False; sample answer: the graph of checking one bag. x > 2 and x > 5 is a ray bounded only on one end. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. b. If Drew’s bag weighs 68 pounds, how much will 56. The graph of a compound inequality involving an or he pay to take it on the plane? statement contains a region of values that are not solutions. ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true.

ANSWER: ANSWER: True a. b. $25 58. WRITING IN MATH An alternate definition of absolute value is to define as the distance 53. ERROR ANALYSIS David and Sarah are solving between a and b on the number line. Explain how . Is either of them this definition can be used to solve inequalities of the correct? Explain your reasoning. form .

ANSWER: Sample answer: represents the distance between some unknown value of the variable x and a point c on the number line. The solution set of the inequality is the set of all numbers ANSWER: such that the distance from the numbers to c is less Sample answer: David; when Sarah converted the than r units. Use a number line to find the numbers absolute value into two inequalities, she mistakenly that are r units from c in either direction. switched the inequality symbols. 59. REASONING The graphs of the solutions of two different absolute value inequalities are shown. 54. CHALLENGE Solve Compare and contrast the absolute value inequalities.

ANSWER:

x < 0 eSolutions Manual - Powered by Cognero Page 6 REASONING Determine whether each statement is true or false . If false, provide a ANSWER: counterexample. Sample answer: The graph on the left indicates a 55. The graph of a compound inequality involving an and solution set from –3 to 5. The statement is bounded on the left and right by two graph on the right indicates a solution values of x. set of all numbers less than or equal to –3 or greater than or equal to 5. ANSWER: False; sample answer: the graph of 60. OPEN ENDED Write an absolute value inequality x > 2 and x > 5 is a ray bounded only on one end. with a solution of ANSWER: 56. The graph of a compound inequality involving an or Sample answer: statement contains a region of values that are not solutions. ANSWER: False; sample answer: the graph of 61. WHICH ONE DOESN’T BELONG? Identify the x > 2 or x < 3 includes the entire number line. compound inequality that is not the same as the other three. Explain your reasoning. 57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true.

ANSWER: True ANSWER: Each of these has a non-empty solution set except 58. WRITING IN MATH An alternate definition of for x > 5 and x < 1. There are no values of x that are absolute value is to define as the distance simultaneously greater than 5 and less than 1. between a and b on the number line. Explain how 62. WRITING IN MATH Summarize the difference this definition can be used to solve inequalities of the between and compound inequalities and or

form . compound inequalities. ANSWER: ANSWER: Sample answer: represents Sample answer: A compound inequality that contains the distance between some unknown value of the and is true if and only if both individual inequalities variable x and a point c on the number line. The are true, while an inequality containing or only needs solution set of the inequality is the set of all numbers one of the individual inequalities to be true. such that the distance from the numbers to c is less 63. Which of the following best describes the graph of than r units. Use a number line to find the numbers the equations below? that are r units from c in either direction.

59. REASONING The graphs of the solutions of two different absolute value inequalities are shown. A The lines have the same x-intercept. Compare and contrast the absolute value inequalities. B The lines have the same y-intercept. C The lines are parallel. D The lines are perpendicular. ANSWER: ANSWER: C Sample answer: The graph on the left indicates a 64. SAT/ACT Find an expression equivalent solution set from –3 to 5. The graph on the right indicates a solution set of all numbers less than or equal to to –3 or greater than or equal to 5.

60. OPEN ENDED Write an absolute value inequality F with a solution of G ANSWER: Sample answer: H

J 61. WHICH ONE DOESN’T BELONG? Identify the compound inequality that is not the same as the other three. Explain your reasoning. K

ANSWER: K ANSWER: Each of these has a non-empty solution set except 65. GRIDDED RESPONSE How many cubes that for x > 5 and x < 1. There are no values of x that are measure 4 centimeters on each side can be placed simultaneously greater than 5 and less than 1. completely inside the box below?

62. WRITING IN MATH Summarize the difference between and compound inequalities and or compound inequalities. ANSWER: Sample answer: A compound inequality that contains ANSWER: and is true if and only if both individual inequalities are true, while an inequality containing or only needs 60

one of the individual inequalities to be true. 66. Which graph represents the solution set for 63. Which of the following best describes the graph of the equations below? A B A The lines have the same x-intercept. B The lines have the same y-intercept. C C The lines are parallel. D D The lines are perpendicular. ANSWER: ANSWER: A C 67. HEALTH The National Heart Association 64. SAT/ACT Find an expression equivalent recommends that less than 30% of a person’s total daily caloric intake come from fat. One gram of fat to yields nine Calories. Consider a healthy 21-year-old whose average caloric intake is between 2500 and 3300 Calories. F a. Write an inequality that represents the suggested fat intake for the person. b G . What is the greatest suggested fat intake for the person?

H ANSWER: a. b.110g J 68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. K Her plane ticket is $375, and the hotel is $85 per

night. a. Let f represent the cost of food for one day. Write ANSWER: an inequality to represent this situation. K b. Solve the inequality and interpret the solution. ANSWER: 65. GRIDDED RESPONSE How many cubes that measure 4 centimeters on each side can be placed a. completely inside the box below? b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER:

ANSWER: 60 70. 66. Which graph represents the solution set for ANSWER:

B 71.

C ANSWER: D

ANSWER: Name the property illustrated by each A statement. 72. If then 67. HEALTH The National Heart Association recommends that less than 30% of a person’s total ANSWER: daily caloric intake come from fat. One gram of fat Addition (=) yields nine Calories. Consider a healthy 21-year-old whose average caloric intake is between 2500 and 3300 Calories. 73. If and then a. Write an inequality that represents the suggested fat intake for the person. ANSWER: b . What is the greatest suggested fat intake for the Transitive (=) person? ANSWER: 74. If then a. ANSWER: b.110g Assoc. (+) 68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. Her plane ticket is $375, and the hotel is $85 per night. a. Let f represent the cost of food for one day. Write an inequality to represent this situation. b. Solve the inequality and interpret the solution. ANSWER: a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER:

70.

ANSWER:

71.

ANSWER:

Name the property illustrated by each statement. 72. If then ANSWER: Addition (=)

73. If and then

ANSWER: Transitive (=)

74. If then

ANSWER: Assoc. (+) Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

2. ANSWER:

3. or ANSWER:

4. or ANSWER:

5. ANSWER:

6. ANSWER:

Solve each inequality. Graph the solution set on a number line. 7. 1. ANSWER: ANSWER:

2. ANSWER:

ANSWER:

9. ANSWER: 3. or

ANSWER:

10. 4. or ANSWER: ANSWER:

11. MONEY Khalid is considering several types of paint

5. for his bedroom. He estimates that he will need ANSWER: between 2 and 3 gallons. The table at the right shows the price per gallon for each type of paint Khalid is

considering. Write a compound inequality and determine how much he could be spending.

6. ANSWER:

7. ANSWER: between $43.96 and $77.94 ANSWER: Solve each inequality. Graph the solution set on a number line. 12. ANSWER: 8. ANSWER:

13. 9. ANSWER: ANSWER:

14. or ANSWER: 10. ANSWER:

15. or

11. MONEY Khalid is considering several types of paint ANSWER: for his bedroom. He estimates that he will need between 2 and 3 gallons. The table at the right shows the price per gallon for each type of paint Khalid is considering. Write a compound inequality and determine how much he could be spending. 16.

ANSWER:

17.

ANSWER: ANSWER: between $43.96 and $77.94

Solve each inequality. Graph the solution set on a number line. 12. 18. ANSWER: ANSWER:

13. 19. ANSWER: ANSWER:

14. or ANSWER: 20.

ANSWER:

15. or

ANSWER: 21.

ANSWER:

16. ANSWER: 22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 17. centimeters. Write an inequality to represent the height of a woman given the length of her femur ANSWER: bone. b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value inequality that describes the woman’s height in centimeters. 18. ANSWER: ANSWER: a. b.

Write an absolute value inequality for each graph.

19. 23. ANSWER: ANSWER:

24. ANSWER: 20.

ANSWER:

25. ANSWER:

21. 26. ANSWER: ANSWER:

27. 22. ANATOMY Forensic scientists use the equation h ANSWER: = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the 28. height of a woman given the length of her femur ANSWER: bone. b. If the length of a female skeleton’s femur is 50 centimeters, write and solve an absolute value inequality that describes the woman’s height in 29. centimeters. ANSWER: ANSWER:

a. b. 30. Write an absolute value inequality for each graph. ANSWER:

23. ANSWER: 31. DOGS The Labrador retriever is one of the most recognized and popular dogs kept as a pet. Using the information given, write a compound inequality to describe the range of healthy weights for a fully grown female Labrador retriever. 24. ANSWER:

25. ANSWER: ANSWER:

32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is 26. greater than the measure of either of its corresponding remote interior angles. Write two ANSWER: inequalities to express the relationships among the measures of the angles of ABC.

27. ANSWER:

ANSWER: 28. ANSWER: Solve each inequality. Graph the solution set on a number line. 33. 29. ANSWER: ANSWER:

30. 34. ANSWER: ANSWER:

31. DOGS The Labrador retriever is one of the most recognized and popular dogs kept as a pet. Using the information given, write a compound inequality to 35. describe the range of healthy weights for a fully grown female Labrador retriever. ANSWER:

36.

ANSWER: ANSWER:

32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is greater than the measure of either of its corresponding remote interior angles. Write two 37. inequalities to express the relationships among the ANSWER: measures of the angles of ABC.

38.

ANSWER: ANSWER:

Solve each inequality. Graph the solution set on a number line. 33. 39. ANSWER: ANSWER:

34.

ANSWER: 40.

ANSWER:

35. ANSWER:

Write an algebraic expression to represent each verbal expression. 41. numbers that are at least 4 units from –5 36. ANSWER: ANSWER:

42. numbers that are no more than unit from 1

ANSWER:

37. ANSWER:

43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER: 38. ANSWER: AUTO RACING 44. NASCAR rules stipulate that a car must conform to a set of 32 templates, each shaped to fit a different contour of the car. When a template is placed on a car, the gap between it and the car cannot exceed the specified tolerance. Each template is marked on its edge with a colored line . 39. that indicates the tolerance for the template

ANSWER:

a. Suppose a certain template is 24.42 inches long. 40. Use the information in the table at the right to write an absolute value inequality for templates with each ANSWER: line color. b. Find the acceptable lengths for that part of a car if the template has each line color. c. Graph the solution set for each line color on a number line. d. The tolerance of which line color includes the Write an algebraic expression to represent tolerances of the other line colors? each verbal expression. Explain your reasoning. 41. numbers that are at least 4 units from –5 ANSWER: ANSWER: a.

42. numbers that are no more than unit from 1 b.

ANSWER: c.

43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER:

44. AUTO RACING NASCAR rules stipulate that a car must conform to a set of 32 templates, each d. Red; the red line color has the smallest tolerance, shaped to fit a different contour of the car. When a , so the other line colors would be template is placed on a car, the gap between it and well within their tolerances. the car cannot exceed the specified tolerance. Each template is marked on its edge with a colored line Solve each inequality. Graph the solution set on that indicates the tolerance for the template. a number line. 45. ANSWER:

46. a. Suppose a certain template is 24.42 inches long. Use the information in the table at the right to write ANSWER: an absolute value inequality for templates with each line color. b. Find the acceptable lengths for that part of a car if the template has each line color. c. Graph the solution set for each line color on a 47. number line. d. The tolerance of which line color includes the ANSWER: tolerances of the other line colors? Explain your reasoning. ANSWER: a. 48. ANSWER:

c. 49. ANSWER:

50. d. Red; the red line color has the smallest tolerance, , so the other line colors would be ANSWER: well within their tolerances.

Solve each inequality. Graph the solution set on a number line. 45. 51. HEALTH Hypoglycemia (low blood sugar) and ANSWER: hyperglycemia (high blood sugar) are potentially dangerous and occur when a person’s blood sugar fluctuates by more than 38 mg from the normal blood sugar level of 88 mg. Write and solve an absolute value inequality to describe blood sugar levels that are considered potentially dangerous. 46. ANSWER: ANSWER:

52. AIR TRAVEL The airline on which Drew is flying has weight restrictions for checked baggage. Drew is checking one bag. 47. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. ANSWER: b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane?

48. ANSWER:

ANSWER: 49. a. b. $25 ANSWER: 53. ERROR ANALYSIS David and Sarah are solving . Is either of them correct? Explain your reasoning.

50. ANSWER:

ANSWER: Sample answer: David; when Sarah converted the absolute value into two inequalities, she mistakenly 51. HEALTH Hypoglycemia (low blood sugar) and switched hyperglycemia (high blood sugar) are potentially the inequality symbols. dangerous and occur when a person’s blood sugar fluctuates by more than 38 mg from the normal blood 54. CHALLENGE Solve sugar level of 88 mg. Write and solve an absolute value inequality to describe blood sugar levels that ANSWER: are considered potentially dangerous. x < 0 ANSWER: REASONING Determine whether each statement is true or false . If false, provide a counterexample. 52. AIR TRAVEL The airline on which Drew is flying 55. The graph of a compound inequality involving an and has weight restrictions for checked baggage. Drew is statement is bounded on the left and right by two checking one bag. values of x. a. Describe the range of weights that would classify ANSWER: Drew’s bag as free, $25, $50, and unacceptable. b. If Drew’s bag weighs 68 pounds, how much will False; sample answer: the graph of he pay to take it on the plane? x > 2 and x > 5 is a ray bounded only on one end.

56. The graph of a compound inequality involving an or statement contains a region of values that are not solutions. ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and ANSWER: statement includes values that make all parts of the a. given statement true. b. $25 ANSWER: True 53. ERROR ANALYSIS David and Sarah are solving . Is either of them 58. WRITING IN MATH An alternate definition of correct? Explain your reasoning. absolute value is to define as the distance between a and b on the number line. Explain how this definition can be used to solve inequalities of the form .

ANSWER:

Sample answer: represents ANSWER: the distance between some unknown value of the Sample answer: David; when Sarah converted the variable x and a point c on the number line. The absolute value into two inequalities, she mistakenly solution set of the inequality is the set of all numbers

switched such that the distance from the numbers to c is less

the inequality symbols. than r units. Use a number line to find the numbers that are r units from c in either direction. 54. CHALLENGE Solve 59. REASONING The graphs of the solutions of two ANSWER: different absolute value inequalities are shown. x < 0 Compare and contrast the absolute value inequalities. REASONING Determine whether each statement is true or false . If false, provide a counterexample. 55. The graph of a compound inequality involving an and statement is bounded on the left and right by two ANSWER: values of x. Sample answer: The graph on the left indicates a

ANSWER: solution set from –3 to 5. The graph on the right indicates a solution False; sample answer: the graph of set of all numbers less than or equal to x > 2 and x > 5 is a ray bounded only on one end. –3 or greater than or equal to 5.

56. The graph of a compound inequality involving an or 60. OPEN ENDED Write an absolute value inequality statement contains a region of values that are not with a solution of solutions. ANSWER: ANSWER: Sample answer: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and 61. WHICH ONE DOESN’T BELONG? Identify the statement includes values that make all parts of the compound inequality that is not the same as the other given statement true. three. Explain your reasoning. ANSWER: True

58. WRITING IN MATH An alternate definition of absolute value is to define as the distance ANSWER: between a and b on the number line. Explain how Each of these has a non-empty solution set except this definition can be used to solve inequalities of the for x > 5 and x < 1. There are no values of x that are form . simultaneously greater than 5 and less than 1.

ANSWER: 62. WRITING IN MATH Summarize the difference between and compound inequalities and or Sample answer: represents compound inequalities. the distance between some unknown value of the variable x and a point c on the number line. The ANSWER: solution set of the inequality is the set of all numbers Sample answer: A compound inequality that contains such that the distance from the numbers to c is less and is true if and only if both individual inequalities 1-6 Solvingthan r units. Compound Use a number and Absolute line to find Value the numbers Inequalities are true, while an inequality containing or only needs that are r units from c in either direction. one of the individual inequalities to be true.

59. REASONING The graphs of the solutions of two 63. Which of the following best describes the graph of different absolute value inequalities are shown. the equations below? Compare and contrast the absolute value inequalities.

A The lines have the same x-intercept. B The lines have the same y-intercept. C The lines are parallel. ANSWER: D The lines are perpendicular. Sample answer: The graph on the left indicates a ANSWER: solution set from –3 to 5. The graph on the right indicates a solution C set of all numbers less than or equal to –3 or greater than or equal to 5. 64. SAT/ACT Find an expression equivalent

60. OPEN ENDED Write an absolute value inequality to with a solution of

ANSWER: F Sample answer:

61. WHICH ONE DOESN’T BELONG? Identify the H compound inequality that is not the same as the other

three. Explain your reasoning. J

ANSWER: Each of these has a non-empty solution set except ANSWER: for x > 5 and x < 1. There are no values of x that are K simultaneously greater than 5 and less than 1. 65. GRIDDED RESPONSE How many cubes that 62. WRITING IN MATH Summarize the difference measure 4 centimeters on each side can be placed between and compound inequalities and or completely inside the box below? compound inequalities. ANSWER: Sample answer: A compound inequality that contains and is true if and only if both individual inequalities are true, while an inequality containing or only needs one of the individual inequalities to be true. ANSWER: 63. Which of the following best describes the graph of 60 the equations below? 66. Which graph represents the solution set for

A The lines have the same x-intercept. A B The lines have the same y-intercept. C The lines are parallel. B eSolutionsD TheManual lines- Poweredare perpendicular.by Cognero Page 7 C ANSWER: C D ANSWER: 64. SAT/ACT Find an expression equivalent A to 67. HEALTH The National Heart Association recommends that less than 30% of a person’s total daily caloric intake come from fat. One gram of fat F yields nine Calories. Consider a healthy 21-year-old whose average caloric intake is between 2500 and G 3300 Calories. a. Write an inequality that represents the suggested fat intake for the person. H b. What is the greatest suggested fat intake for the

person? J ANSWER: a. K b.110g

68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. ANSWER: Her plane ticket is $375, and the hotel is $85 per K night. a. Let f represent the cost of food for one day. Write 65. GRIDDED RESPONSE How many cubes that an inequality to represent this situation. measure 4 centimeters on each side can be placed b. Solve the inequality and interpret the solution. completely inside the box below? ANSWER: a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69. ANSWER: 60 ANSWER:

66. Which graph represents the solution set for

70. A ANSWER: B C D 71.

ANSWER: ANSWER: A HEALTH 67. The National Heart Association Name the property illustrated by each recommends that less than 30% of a person’s total statement. daily caloric intake come from fat. One gram of fat 72. If then yields nine Calories. Consider a healthy 21-year-old whose average caloric intake is between 2500 and ANSWER: 3300 Calories. Addition (=) a. Write an inequality that represents the suggested fat intake for the person. b. What is the greatest suggested fat intake for the 73. If and then person? ANSWER: ANSWER: a. Transitive (=) b.110g 74. If then 68. TRAVEL Maggie is planning a 5-day trip to a family reunion. She wants to spend no more than $1000. ANSWER: Her plane ticket is $375, and the hotel is $85 per Assoc. (+) night. a. Let f represent the cost of food for one day. Write an inequality to represent this situation. b. Solve the inequality and interpret the solution. ANSWER: a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER:

70.

ANSWER:

71.

ANSWER:

Name the property illustrated by each statement. 72. If then ANSWER: Addition (=)

73. If and then

ANSWER: Transitive (=)

74. If then

ANSWER: Assoc. (+) Solve each inequality. Graph the solution set on a number line. 1. ANSWER:

2. ANSWER:

3. or ANSWER:

4. or ANSWER:

5. ANSWER:

6. ANSWER:

7. Solve each inequality. Graph the solution set on a number line. ANSWER: 1. ANSWER:

8. ANSWER:

2. ANSWER: 9. ANSWER:

3. or ANSWER:

10. ANSWER: 4. or ANSWER:

6. ANSWER:

ANSWER: between $43.96 and $77.94 7. Solve each inequality. Graph the solution set on ANSWER: a number line. 12. ANSWER:

8. ANSWER: 13. ANSWER:

9. ANSWER:

14. or ANSWER:

10. ANSWER: 15. or ANSWER:

17. ANSWER:

ANSWER: between $43.96 and $77.94

Solve each inequality. Graph the solution set on 18. a number line. ANSWER: 12.

ANSWER:

19.

13. ANSWER:

ANSWER:

20. 14. or ANSWER: ANSWER:

15. or 21. ANSWER: ANSWER:

16. 22. ANATOMY Forensic scientists use the equation h ANSWER: = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. a. Suppose the equation has a margin of error of ±3 centimeters. Write an inequality to represent the height of a woman given the length of her femur 17. bone. b. If the length of a female skeleton’s femur is 50 ANSWER: centimeters, write and solve an absolute value inequality that describes the woman’s height in centimeters. ANSWER: 18. a. b. ANSWER: Write an absolute value inequality for each graph. 23. ANSWER: 19.

ANSWER:

24. ANSWER:

20. ANSWER: 25. ANSWER:

26. 21. ANSWER: ANSWER:

27. ANSWER:

22. ANATOMY Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone. 28. a . Suppose the equation has a margin of error of ±3 ANSWER: centimeters. Write an inequality to represent the height of a woman given the length of her femur bone. b. If the length of a female skeleton’s femur is 50 29. centimeters, write and solve an absolute value inequality that describes the woman’s height in ANSWER: centimeters. ANSWER: a. 30. b. ANSWER: Write an absolute value inequality for each graph. 31. DOGS The Labrador retriever is one of the most 23. recognized and popular dogs kept as a pet. Using the ANSWER: information given, write a compound inequality to describe the range of healthy weights for a fully

grown female Labrador retriever.

24. ANSWER:

ANSWER: 25. ANSWER: 32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is greater than the measure of either of its corresponding remote interior angles. Write two 26. inequalities to express the relationships among the measures of the angles of ABC. ANSWER:

27.

ANSWER: ANSWER:

28. Solve each inequality. Graph the solution set on a number line. ANSWER: 33.

ANSWER:

29. ANSWER:

34. 30. ANSWER: ANSWER:

36. ANSWER:

ANSWER:

32. GEOMETRY The Exterior Angle Inequality Theorem states that an exterior angle measure is 37. greater than the measure of either of its ANSWER: corresponding remote interior angles. Write two inequalities to express the relationships among the measures of the angles of ABC.

38. ANSWER:

ANSWER:

Solve each inequality. Graph the solution set on a number line. 39. 33. ANSWER: ANSWER:

34. 40. ANSWER: ANSWER:

35. ANSWER: Write an algebraic expression to represent each verbal expression. 41. numbers that are at least 4 units from –5 ANSWER: 36. ANSWER: 42. numbers that are no more than unit from 1

ANSWER:

37. ANSWER: 43. numbers that are at least 6 units but no more than 10 units from 2

ANSWER:

39.

ANSWER:

42. numbers that are no more than unit from 1 c. ANSWER:

43. numbers that are at least 6 units but no more than 10 units from 2 ANSWER:

46.

49. c. ANSWER:

50.

ANSWER: d. Red; the red line color has the smallest tolerance, , so the other line colors would be well within their tolerances.

Solve each inequality. Graph the solution set on 51. HEALTH Hypoglycemia (low blood sugar) and a number line. hyperglycemia (high blood sugar) are potentially 45. dangerous and occur when a person’s blood sugar fluctuates by more than 38 mg from the normal blood ANSWER: sugar level of 88 mg. Write and solve an absolute value inequality to describe blood sugar levels that are considered potentially dangerous. ANSWER:

46. ANSWER: 52. AIR TRAVEL The airline on which Drew is flying has weight restrictions for checked baggage. Drew is checking one bag. a. Describe the range of weights that would classify Drew’s bag as free, $25, $50, and unacceptable. 47. b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane? ANSWER:

48. ANSWER:

ANSWER: a. b. $25 49. 53. ERROR ANALYSIS David and Sarah are solving ANSWER: . Is either of them

correct? Explain your reasoning.

50.

ANSWER: ANSWER:

Sample answer: David; when Sarah converted the absolute value into two inequalities, she mistakenly switched the inequality symbols. 51. HEALTH Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially 54. CHALLENGE Solve dangerous and occur when a person’s blood sugar fluctuates by more than 38 mg from the normal blood ANSWER: sugar level of 88 mg. Write and solve an absolute x < 0 value inequality to describe blood sugar levels that are considered potentially dangerous. REASONING Determine whether each ANSWER: statement is true or false . If false, provide a counterexample. 55. The graph of a compound inequality involving an and statement is bounded on the left and right by two 52. AIR TRAVEL The airline on which Drew is flying values of x. has weight restrictions for checked baggage. Drew is ANSWER: checking one bag. a. Describe the range of weights that would classify False; sample answer: the graph of Drew’s bag as free, $25, $50, and unacceptable. x > 2 and x > 5 is a ray bounded only on one end. b. If Drew’s bag weighs 68 pounds, how much will he pay to take it on the plane? 56. The graph of a compound inequality involving an or statement contains a region of values that are not solutions. ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line.

57. The graph of a compound inequality involving an and statement includes values that make all parts of the given statement true. ANSWER: ANSWER: a. True b. $25 58. WRITING IN MATH An alternate definition of 53. ERROR ANALYSIS David and Sarah are solving absolute value is to define as the distance . Is either of them between a and b on the number line. Explain how correct? Explain your reasoning. this definition can be used to solve inequalities of the form .

ANSWER: Sample answer: represents the distance between some unknown value of the variable x and a point c on the number line. The ANSWER: solution set of the inequality is the set of all numbers Sample answer: David; when Sarah converted the such that the distance from the numbers to c is less absolute value into two inequalities, she mistakenly than r units. Use a number line to find the numbers switched that are r units from c in either direction. the inequality symbols. 59. REASONING The graphs of the solutions of two 54. CHALLENGE Solve different absolute value inequalities are shown. Compare and contrast the absolute value inequalities. ANSWER: x < 0

REASONING Determine whether each

statement is true or false . If false, provide a counterexample. ANSWER: 55. The graph of a compound inequality involving an and Sample answer: The graph on the left indicates a statement is bounded on the left and right by two solution set from –3 to 5. The values of x. graph on the right indicates a solution set of all numbers less than or equal to ANSWER: –3 or greater than or equal to 5. False; sample answer: the graph of x > 2 and x > 5 is a ray bounded only on one end. 60. OPEN ENDED Write an absolute value inequality with a solution of 56. The graph of a compound inequality involving an or ANSWER: statement contains a region of values that are not solutions. Sample answer: ANSWER: False; sample answer: the graph of x > 2 or x < 3 includes the entire number line. 61. WHICH ONE DOESN’T BELONG? Identify the compound inequality that is not the same as the other 57. The graph of a compound inequality involving an and three. Explain your reasoning. statement includes values that make all parts of the

given statement true. ANSWER:

True ANSWER: 58. WRITING IN MATH An alternate definition of Each of these has a non-empty solution set except absolute value is to define as the distance for x > 5 and x < 1. There are no values of x that are between a and b on the number line. Explain how simultaneously greater than 5 and less than 1. this definition can be used to solve inequalities of the 62. WRITING IN MATH Summarize the difference form . between and compound inequalities and or ANSWER: compound inequalities. Sample answer: represents ANSWER: the distance between some unknown value of the Sample answer: A compound inequality that contains variable x and a point c on the number line. The and is true if and only if both individual inequalities solution set of the inequality is the set of all numbers are true, while an inequality containing or only needs such that the distance from the numbers to c is less one of the individual inequalities to be true. than r units. Use a number line to find the numbers that are r units from c in either direction. 63. Which of the following best describes the graph of the equations below? 59. REASONING The graphs of the solutions of two different absolute value inequalities are shown. Compare and contrast the absolute value inequalities. A The lines have the same x-intercept. B The lines have the same y-intercept. C The lines are parallel. D The lines are perpendicular.

ANSWER: ANSWER: Sample answer: The graph on the left indicates a C solution set from –3 to 5. The 64. SAT/ACT Find an expression equivalent graph on the right indicates a solution set of all numbers less than or equal to –3 or greater than or equal to 5. to

60. OPEN ENDED Write an absolute value inequality F with a solution of ANSWER: G Sample answer:

61. WHICH ONE DOESN’T BELONG? Identify the J compound inequality that is not the same as the other three. Explain your reasoning. K

ANSWER: ANSWER: K Each of these has a non-empty solution set except for x > 5 and x < 1. There are no values of x that are 65. GRIDDED RESPONSE How many cubes that simultaneously greater than 5 and less than 1. measure 4 centimeters on each side can be placed completely inside the box below? 62. WRITING IN MATH Summarize the difference between and compound inequalities and or compound inequalities. ANSWER: Sample answer: A compound inequality that contains and is true if and only if both individual inequalities are true, while an inequality containing or only needs ANSWER: one of the individual inequalities to be true. 60

63. Which of the following best describes the graph of 66. Which graph represents the solution set for the equations below?

A The lines have the same x-intercept. B B The lines have the same y-intercept. C The lines are parallel. C D The lines are perpendicular. D ANSWER: ANSWER: C A 64. SAT/ACT Find an expression equivalent 67. HEALTH The National Heart Association

recommends that less than 30% of a person’s total to daily caloric intake come from fat. One gram of fat yields nine Calories. Consider a healthy 21-year-old whose average caloric intake is between 2500 and F 3300 Calories. a . Write an inequality that represents the suggested G fat intake for the person. b. What is the greatest suggested fat intake for the person? H ANSWER: a. J b.110g

Solve each equation. Check your solutions. 69.

ANSWER: 1-6 SolvingANSWER: Compound and Absolute Value Inequalities 60

66. Which graph represents the solution set for 70.

ANSWER: A B

C 71. D ANSWER:

ANSWER: A Name the property illustrated by each statement. HEALTH 67. The National Heart Association 72. If then recommends that less than 30% of a person’s total daily caloric intake come from fat. One gram of fat ANSWER: yields nine Calories. Consider a healthy 21-year-old Addition (=) whose average caloric intake is between 2500 and 3300 Calories. a. Write an inequality that represents the suggested 73. If and then fat intake for the person. b . What is the greatest suggested fat intake for the ANSWER: person? Transitive (=) ANSWER: a. 74. If then b.110g ANSWER: 68. TRAVEL Maggie is planning a 5-day trip to a family Assoc. (+) reunion. She wants to spend no more than $1000. Her plane ticket is $375, and the hotel is $85 per night. a. Let f represent the cost of food for one day. Write an inequality to represent this situation. b. Solve the inequality and interpret the solution. ANSWER: a. b. She can spend no more than $40 per day on food.

Solve each equation. Check your solutions. 69.

ANSWER:

70.

ANSWER:

eSolutions Manual - Powered by Cognero Page 8 71.

ANSWER:

Name the property illustrated by each statement. 72. If then ANSWER: Addition (=)

73. If and then

ANSWER: Transitive (=)

74. If then

ANSWER: Assoc. (+) Write each inequality using interval notation. 1. ANSWER:

ANSWER:

ANSWER: (1, 3)

ANSWER:

ANSWER: (–3, 4)

9. ANSWER: Explore 1-6 Explore Algebra Lab: Interval Notation

Write each inequality using interval notation. 1. 10. ANSWER: ANSWER:

2. 11. ANSWER: ANSWER: (–8, 8)

3. 12. ANSWER: ANSWER:

ANSWER: 13. ANSWER:

ANSWER: (1, 3) 14. ANSWER: 6.

ANSWER: Graph each solution set on a number line. 15. 7. ANSWER: ANSWER:

16. 8. ANSWER: ANSWER: (–3, 4)

17. 9. ANSWER: ANSWER:

18. WRITING IN MATH Write in words the meaning 10. of Then write the compound inequality that this notation represents. eSolutionsANSWER: Manual - Powered by Cognero Page 1 ANSWER: All values less than 3, not including 3, are part of the solution set. All values greater than and including 10 11. are part of the solution set;

ANSWER: 19. WRITING IN MATH How are symbols used to (–8, 8) write solution sets for inequalities? Explain. ANSWER: 12. Sample answer: Infinity symbols are used to indicate whether a set is unbounded in the positive or negative ANSWER: direction; a parenthesis is used to indicate that an endpoint is not included in the set; a bracket is used to indicate that an endpoint is included in the set; a union symbol is used to indicate the union of two sets. 13. ANSWER:

14. ANSWER:

Graph each solution set on a number line. 15. ANSWER:

16.

ANSWER:

17. ANSWER:

18. WRITING IN MATH Write in words the meaning of Then write the compound inequality that this notation represents. ANSWER: All values less than 3, not including 3, are part of the solution set. All values greater than and including 10 are part of the solution set;

19. WRITING IN MATH How are symbols used to write solution sets for inequalities? Explain. ANSWER: Sample answer: Infinity symbols are used to indicate whether a set is unbounded in the positive or negative direction; a parenthesis is used to indicate that an endpoint is not included in the set; a bracket is used to indicate that an endpoint is included in the set; a union symbol is used to indicate the union of two sets. Write each inequality using interval notation. 1. ANSWER:

ANSWER:

ANSWER: (1, 3)

ANSWER:

ANSWER: (–3, 4)

9. ANSWER:

10. ANSWER:

11. ANSWER: (–8, 8)

12. ANSWER:

13. ANSWER:

14. ANSWER:

Graph each solution set on a number line. 15. ANSWER:

16.

ANSWER:

17. ANSWER: Explore 1-6 Explore Algebra Lab: Interval Notation