Write an Algebraic Expression to Represent Each Verbal Expression. 1

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Write an algebraic expression to represent each verbal expression. 1. the product of 12 and the sum of a number and negative 3 ANSWER:

2. the difference between the product of 4 and a number and the square of the number ANSWER: 2 4x – x

Write a verbal sentence to represent each equation. 3. ANSWER: The sum of five times a number and 7 equals 18.

4. ANSWER: The difference between the square of a number and 9 is 27.

5. ANSWER: The difference between five times a number and the cube of that number is 12.

ANSWER: Eight more than the quotient of a number and four is –16.

Name the property illustrated by each statement. 7.

ANSWER: Reflexive Property

8. If and , then . 1-3 Solving Equations ANSWER: Transitive Property

Write an algebraic expression to represent Solve each equation. Check your solution. each verbal expression. 9. 1. the product of 12 and the sum of a number and negative 3 ANSWER: 53 ANSWER:

10. ANSWER: 2. the difference between the product of 4 and a number and the square of the number –6

ANSWER: 11. 2 4x – x ANSWER: Write a verbal sentence to represent each –8 equation. 3. 12. ANSWER: ANSWER: The sum of five times a number and 7 equals 18. –7

4. 13. ANSWER: ANSWER: The difference between the square of a number and –6 9 is 27. 14. 5. ANSWER: ANSWER: –4 The difference between five times a number and the cube of that number is 12. 15.

ANSWER: 6. 3 ANSWER: Eight more than the quotient of a number and four is 16.

–16. ANSWER: Name the property illustrated by each 8 statement. 7. 17.

ANSWER: ANSWER: Reflexive Property 4

8. If and , then . 18. ANSWER: ANSWER: Transitive Property –5 eSolutions Manual - Powered by Cognero Page 1 Solve each equation. Check your solution. Solve each equation or formula for the specified 9. variable. ANSWER: 19. ,for q 53 ANSWER:

10. ANSWER: –6 20. , for n ANSWER: 11.

ANSWER: –8 21. MULTIPLE CHOICE If , what is the 12.

ANSWER: value of ? –7 A –10 B –3 13. C 1 ANSWER: D 5 –6 ANSWER: B 14. ANSWER: Write an algebraic expression to represent each verbal expression. –4 22. the difference between the product of four and a number and 6 15. ANSWER: ANSWER: 3 23. the product of the square of a number and 8 16. ANSWER: ANSWER: 8x2 8 24. fifteen less than the cube of a number 17. ANSWER: 3 ANSWER: x – 15

4 25. five more than the quotient of a number and 4 18. ANSWER:

ANSWER: –5 Write a verbal sentence to represent each Solve each equation or formula for the specified equation. variable. 26. 19. ,for q ANSWER: ANSWER: Four less than 8 times a number is 16.

27.

20. , for n ANSWER: ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

28.

21. MULTIPLE CHOICE If , what is the ANSWER: Three less than four times the square of a number is

value of ? 13. A –10 29. BASEBALL During a recent season, Miguel B –3 Cabrera and Mike Jacobs of the Florida Marlins hit a C 1 combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did D 5 each player hit? Define a variable, write an equation, ANSWER: and solve the problem. B ANSWER: n = number of home runs Jacobs hit; n + 6 = number Write an algebraic expression to represent of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 each verbal expression. home runs, Cabrera: 26 home runs. 22. the difference between the product of four and a number and 6 Name the property illustrated by each ANSWER: statement. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9

ANSWER: 23. the product of the square of a number and 8 30. Subtr. (=)

ANSWER: 31. If y = –3, then 7y = 7(–3) 8x2 ANSWER: 24. fifteen less than the cube of a number Subst. ANSWER: 32. If g = 3h and 3h = 16, then g = 16 3 x – 15 ANSWER: Transitive Property 25. five more than the quotient of a number and 4 ANSWER: 33. If –y = 13, then –(–y) = –13 ANSWER: Mult. (=)

Write a verbal sentence to represent each 34. MONEY Aiko and Kendra arrive at the state fair equation. with $32.50. What is the total number of rides they 26. can go on if they each pay the entrance fee? ANSWER: Four less than 8 times a number is 16.

27.

13. 35. ANSWER: 29. BASEBALL During a recent season, Miguel 5 Cabrera and Mike Jacobs of the Florida Marlins hit a combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did 36. each player hit? Define a variable, write an equation, and solve the problem. ANSWER: –7 ANSWER: n = number of home runs Jacobs hit; n + 6 = number 37. of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 home runs, Cabrera: 26 home runs. ANSWER: –3 Name the property illustrated by each statement. 38. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 ANSWER: ANSWER: –5 30. Subtr. (=) 39.

31. If y = –3, then 7y = 7(–3) ANSWER: ANSWER: –6 Subst. 40. 32. If g = 3h and 3h = 16, then g = 16 ANSWER: ANSWER: 8 Transitive Property

33. If –y = 13, then –(–y) = –13 41. ANSWER: ANSWER: Mult. (=) –3 34. MONEY Aiko and Kendra arrive at the state fair with $32.50. What is the total number of rides they 42. can go on if they each pay the entrance fee? ANSWER: 4

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: s = length of a side; 5s = 100; 20 in.

44. MEDICINE For Nina’s illness her doctor gives her ANSWER: a prescription for 28 pills. The doctor says that she should take 4 pills the first day and then 2 pills each

n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 day until her prescription runs out. For how many

Solve each equation. Check your solution. days does she take 2 pills? 35. ANSWER: ANSWER: x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days 5 Solve each equation or formula for the specified 36. variable. 45. , for m ANSWER: –7 ANSWER:

37. ANSWER: –3 46. , for a

38. ANSWER: ANSWER: –5

39. 47. , for h ANSWER: ANSWER: –6

40. 48. , for y ANSWER: 8 ANSWER:

41. 49. , for a ANSWER: –3 ANSWER:

42. 50. , for z ANSWER: 4 ANSWER:

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: 51. GEOMETRY The formula for the volume of a s = length of a side; 5s = 100; 20 in. cylinder with radius r and height h is times the radius times the height. 44. MEDICINE For Nina’s illness her doctor gives her a. Write this as an algebraic expression. a prescription for 28 pills. The doctor says that she b. Solve the expression in part a for h. should take 4 pills the first day and then 2 pills each day until her prescription runs out. For how many ANSWER: days does she take 2 pills? a. ANSWER: b. x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days 52. AWARDS BANQUET A banquet room can seat a maximum of 69 people. The coach, principal, and Solve each equation or formula for the specified vice principal have invited the award-winning girls’ variable. tennis team to the banquet. If the tennis team 45. , for m consists of 22 girls, how many guests can each student bring? ANSWER: ANSWER: n = number of guests that each student can bring; 22n + 25 = 69; 2 guests

46. , for a Solve each equation. Check your solution. 53. ANSWER: ANSWER: –2

47. , for h 54. ANSWER: ANSWER: 3

55. 48. , for y ANSWER: ANSWER: –4

56. 49. , for a ANSWER: ANSWER: 3

57.

50. , for z ANSWER:

ANSWER:

58. 51. GEOMETRY The formula for the volume of a cylinder with radius r and height h is times the ANSWER: radius times the height. a. Write this as an algebraic expression. b. Solve the expression in part a for h. 59. FINANCIAL LITERACY Benjamin spent $10,734 ANSWER: on his living expenses last year. Most of these a. expenses are listed at the right. Benjamin’s only b. other expense last year was rent. If he paid rent 12 times last year, how much is Benjamin’s rent each month? 52. AWARDS BANQUET A banquet room can seat a maximum of 69 people. The coach, principal, and vice principal have invited the award-winning girls’ tennis team to the banquet. If the tennis team consists of 22 girls, how many guests can each student bring? ANSWER: ANSWER: n = number of guests that each student can bring; x = the cost of rent each month; 622 + 428 + 240 + 22n + 25 = 69; 2 guests 144 + 12x = 10,734; $775 per month

Solve each equation. Check your solution. 60. BRIDGES The Sunshine Skyway Bridge spans 53. Tampa Bay, Florida. Suppose one crew began ANSWER: building south from St. Petersburg, and another crew began building north from Bradenton. The two crews –2 met 10,560 feet south of St. Petersburg approximately 5 years after construction began. a. Suppose the St. Petersburg crew built an average 54. of 176 feet per month. Together the two crews built 21,120 feet of bridge. Determine the average number ANSWER: of feet built per month by the Bradenton crew. 3 b. About how many miles of bridge did each crew build? 55. c. Is this answer reasonable? Explain. ANSWER: ANSWER: –4 a. 176 ft b. 2 mi 56. c. Yes; it seems reasonable that two crews working ANSWER: 4 miles apart would be able to complete the same 3 amount of miles in the same amount of time. 61. MULTIPLE REPRESENTATIONS The absolute 57. value of a number describes the distance of the number from zero. ANSWER: a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the number line and their distance from zero. c. GRAPHICAL Make a graph of each integer x 58. and its distance from zero y using the data points in the table. ANSWER: d. VERBAL Make a conjecture about the integer and its distance from zero. Explain the reason for any changes in sign. ANSWER: 59. FINANCIAL LITERACY Benjamin spent $10,734 a. on his living expenses last year. Most of these expenses are listed at the right. Benjamin’s only

other expense last year was rent. If he paid rent 12 b. times last year, how much is Benjamin’s rent each month?

ANSWER: x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month

61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the number from zero.

a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. ANSWER: b. TABULAR Create a table of the integers on the Sample answer: Jade; in the last step, when Steven number line and their distance from zero. subtracted b1 from each side, he mistakenly put the – c. GRAPHICAL Make a graph of each integer x b in the numerator instead of after the entire and its distance from zero y using the data points in 1 the table. fraction. d. VERBAL Make a conjecture about the integer 63. CHALLENGE Solve and its distance from zero. Explain the reason for any changes in sign. for y1 ANSWER: ANSWER: a.

b. 64. REASONING Use what you have learned in this lesson to explain why the following number trick works. • Take any number. • Multiply it by ten. • Subtract 30 from the result. • Divide the new result by 5. • Add 6 to the result. • Your new number is twice your original. ANSWER: Translating this number trick into an expression yields: c.

65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no solution and another example that has infinitely many d. For positive integers, the distance from zero is the solutions. same as the integer. For negative integers, the ANSWER: distance is the integer with the opposite sign because distance is always positive. Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2 WRITING IN MATH 62. ERROR ANALYSIS Steven and Jade are solving 66. Compare and contrast the Substitution Property of Equality and the Transitive

for b2. Is either of them correct? Property of Equality. Explain your reasoning. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property is done with two values, that is, one being substituted for another, the Transitive Property deals with three values, determining that since two values are equal to ANSWER: a third value, then they must be equal. Sample answer: Jade; in the last step, when Steven 67. The graph shows the solution of which inequality? subtracted b1 from each side, he mistakenly put the –

b1 in the numerator instead of after the entire fraction.

63. CHALLENGE Solve

for y1 ANSWER:

A. C.

64. REASONING Use what you have learned in this B. D. lesson to explain why the following number trick works. ANSWER: • Take any number. D • Multiply it by ten. • Subtract 30 from the result. 68. SAT/ACT What is subtracted from its • Divide the new result by 5. • Add 6 to the result. reciprocal? • Your new number is twice your original. F ANSWER: G Translating this number trick into an expression yields: H

solutions. transformation of to ? ANSWER: Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2

66. WRITING IN MATH Compare and contrast the Substitution Property of Equality and the Transitive Property of Equality. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property A. a reflection across the y-axis and a translation is done with two values, that is, one being substituted down 2 units for another, the Transitive Property deals with three B. a reflection across the x-axis and a translation values, determining that since two values are equal to down 2 units a third value, then they must be equal. C. a rotation to the right and a translation down 2 units 67. The graph shows the solution of which inequality? D. a rotation to the right and a translation right 2 units ANSWER: A

70. SHORT RESPONSE A local theater sold 1200 tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What was the percent decrease of tickets sold?

A. C. ANSWER:

B. D. 71. Simplify . ANSWER: ANSWER: D –3x + 6y + 6z

68. SAT/ACT What is subtracted from its 72. BAKING Tamera is making two types of bread. reciprocal? The first type of bread needs cups of flour, and F the second needs cups of flour. Tamera wants to G make 2 loaves of the first recipe and 3 loaves of the second recipe. How many cups of flour does she H need?

J ANSWER:

LANDMARKS ANSWER: 73. Suppose the Space Needle in Seattle, Washington, casts a 220-foot shadow at the G same time a nearby tourist casts a 2-foot shadow. If 69. GEOMETRY Which of the following describes the the tourist is feet tall, how tall is the Space transformation of to ? Needle?

A. a reflection across the y-axis and a translation down 2 units B. a reflection across the x-axis and a translation ANSWER: down 2 units 605 ft C. a rotation to the right and a translation down 2 units 74. Evaluate , if a = 5, b = 7, and c = 2. D. a rotation to the right and a translation right 2 units ANSWER: 1 ANSWER: A Identify the additive inverse for each number or expression. 70. SHORT RESPONSE A local theater sold 1200 tickets during the opening weekend of a movie. On 75. the following weekend, 840 tickets were sold. What was the percent decrease of tickets sold? ANSWER: ANSWER:

71. Simplify . 76. 3.5 ANSWER: ANSWER: –3x + 6y + 6z

72. BAKING Tamera is making two types of bread. 77. The first type of bread needs cups of flour, and ANSWER: 2x the second needs cups of flour. Tamera wants to 78. make 2 loaves of the first recipe and 3 loaves of the second recipe. How many cups of flour does she ANSWER: need? ANSWER:

79.

ANSWER: 73. LANDMARKS Suppose the Space Needle in Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If the tourist is feet tall, how tall is the Space 80. Needle? ANSWER: 1.25

81. ANSWER:

82. ANSWER:

ANSWER: 605 ft

74. Evaluate , if a = 5, b = 7, and c = 2.

ANSWER: 1 Identify the additive inverse for each number or expression.

75.

ANSWER:

76. 3.5 ANSWER:

77. ANSWER: 2x

78. ANSWER:

79.

ANSWER:

80. ANSWER: 1.25

81. ANSWER:

82. ANSWER:

Write an algebraic expression to represent each verbal expression. 1. the product of 12 and the sum of a number and negative 3 ANSWER:

2. the difference between the product of 4 and a number and the square of the number ANSWER: 2 4x – x

Write a verbal sentence to represent each equation. 3. ANSWER: The sum of five times a number and 7 equals 18.

4. ANSWER: The difference between the square of a number and 9 is 27.

5. ANSWER: The difference between five times a number and the cube of that number is 12.

ANSWER: Eight more than the quotient of a number and four is –16.

Name the property illustrated by each statement. 7.

ANSWER: Reflexive Property

8. If and , then . ANSWER: Write an algebraic expression to represent Transitive Property each verbal expression. 1. the product of 12 and the sum of a number and Solve each equation. Check your solution. negative 3 9. ANSWER: ANSWER: 53

10. 2. the difference between the product of 4 and a number and the square of the number ANSWER: ANSWER: –6 2 4x – x 11. Write a verbal sentence to represent each ANSWER: equation. –8 3. ANSWER: 12. The sum of five times a number and 7 equals 18. ANSWER: –7 4. 13. ANSWER: The difference between the square of a number and ANSWER: 9 is 27. –6

5. 14. ANSWER: ANSWER: The difference between five times a number and the –4 cube of that number is 12.

15. 6. ANSWER: ANSWER: 3 Eight more than the quotient of a number and four is –16. 16.

Name the property illustrated by each ANSWER: statement. 8 7.

ANSWER: 17. Reflexive Property ANSWER: 4 8. If and , then . ANSWER: 18. Transitive Property ANSWER: Solve each equation. Check your solution. –5 9. Solve each equation or formula for the specified ANSWER: variable. 53 19. ,for q ANSWER: 10.

ANSWER: –6 20. , for n 11. ANSWER: ANSWER: –8

12. 21. MULTIPLE CHOICE If , what is the ANSWER:

–7 value of ? A 13. –10 B –3 ANSWER: C 1 –6 D 5 ANSWER: 14. B ANSWER: –4 Write an algebraic expression to represent each verbal expression. 15. 22. the difference between the product of four and a number and 6 ANSWER: ANSWER: 3

16. 23. the product of the square of a number and 8 ANSWER: ANSWER: 8 8x2

17. 24. fifteen less than the cube of a number ANSWER: ANSWER: 1-3 Solving Equations 3 4 x – 15

18. 25. five more than the quotient of a number and 4 ANSWER: ANSWER:

–5

Solve each equation or formula for the specified Write a verbal sentence to represent each variable. equation. 19. ,for q 26. ANSWER: ANSWER: Four less than 8 times a number is 16.

20. , for n 27.

ANSWER: ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

28. 21. MULTIPLE CHOICE If , what is the ANSWER: value of ? Three less than four times the square of a number is 13. A –10 B –3 29. BASEBALL During a recent season, Miguel C 1 Cabrera and Mike Jacobs of the Florida Marlins hit a D 5 combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did ANSWER: each player hit? Define a variable, write an equation, B and solve the problem.

Write an algebraic expression to represent ANSWER: each verbal expression. n = number of home runs Jacobs hit; n + 6 = number 22. the difference between the product of four and a of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 number and 6 home runs, Cabrera: 26 home runs. ANSWER: Name the property illustrated by each statement. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 23. the product of the square of a number and 8 ANSWER: 30. Subtr. (=) ANSWER: 8x2 31. If y = –3, then 7y = 7(–3) 24. fifteen less than the cube of a number ANSWER: ANSWER: Subst. 3 x – 15 32. If g = 3h and 3h = 16, then g = 16 25. five more than the quotient of a number and 4 ANSWER: Transitive Property eSolutionsANSWER: Manual - Powered by Cognero Page 2 33. If –y = 13, then –(–y) = –13 ANSWER: Write a verbal sentence to represent each Mult. (=) equation. MONEY 26. 34. Aiko and Kendra arrive at the state fair with $32.50. What is the total number of rides they ANSWER: can go on if they each pay the entrance fee? Four less than 8 times a number is 16.

27.

ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

and solve the problem. 36. ANSWER: ANSWER: –7 n = number of home runs Jacobs hit; n + 6 = number of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 37. home runs, Cabrera: 26 home runs. ANSWER: Name the property illustrated by each –3 statement. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 38. ANSWER: ANSWER: 30. Subtr. (=) –5

31. If y = –3, then 7y = 7(–3) 39.

ANSWER: ANSWER: Subst. –6 32. If g = 3h and 3h = 16, then g = 16 40. ANSWER: Transitive Property ANSWER: 8 33. If –y = 13, then –(–y) = –13 ANSWER: 41. Mult. (=) ANSWER: 34. MONEY Aiko and Kendra arrive at the state fair –3 with $32.50. What is the total number of rides they can go on if they each pay the entrance fee? 42.

ANSWER: 4

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: s = length of a side; 5s = 100; 20 in. ANSWER: 44. MEDICINE For Nina’s illness her doctor gives her n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 a prescription for 28 pills. The doctor says that she should take 4 pills the first day and then 2 pills each Solve each equation. Check your solution. day until her prescription runs out. For how many 35. days does she take 2 pills? ANSWER: ANSWER: 5 x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days

36. Solve each equation or formula for the specified ANSWER: variable. –7 45. , for m ANSWER: 37.

ANSWER: –3

38. 46. , for a ANSWER: ANSWER: –5

39. 47. , for h ANSWER: –6 ANSWER:

40.

ANSWER: 48. , for y 8 ANSWER: 41.

ANSWER: 49. , for a –3 ANSWER: 42.

ANSWER: 4 50. , for z

43. GEOMETRY The perimeter of a regular pentagon ANSWER: is 100 inches. Find the length of each side. ANSWER: s = length of a side; 5s = 100; 20 in. 51. GEOMETRY The formula for the volume of a cylinder with radius r and height h is times the 44. MEDICINE For Nina’s illness her doctor gives her radius times the height. a prescription for 28 pills. The doctor says that she should take 4 pills the first day and then 2 pills each a. Write this as an algebraic expression. day until her prescription runs out. For how many b. Solve the expression in part a for h. days does she take 2 pills? ANSWER: ANSWER: a. x = the number of days she takes 2 pills; 4 + 2x = 28; b. 12 days

Solve each equation or formula for the specified 52. AWARDS BANQUET A banquet room can seat a variable. maximum of 69 people. The coach, principal, and vice principal have invited the award-winning girls’

45. , for m tennis team to the banquet. If the tennis team ANSWER: consists of 22 girls, how many guests can each student bring? ANSWER: n = number of guests that each student can bring; 22n + 25 = 69; 2 guests 46. , for a Solve each equation. Check your solution. ANSWER: 53. ANSWER: –2 47. , for h

ANSWER: 54.

ANSWER: 3 48. , for y 55. ANSWER: ANSWER: –4

49. , for a 56. ANSWER: ANSWER: 3

57. 50. , for z ANSWER: ANSWER:

51. GEOMETRY The formula for the volume of a 58. cylinder with radius r and height h is times the radius times the height. ANSWER: a. Write this as an algebraic expression. b. Solve the expression in part a for h. ANSWER: 59. FINANCIAL LITERACY Benjamin spent $10,734 a. on his living expenses last year. Most of these b. expenses are listed at the right. Benjamin’s only other expense last year was rent. If he paid rent 12 52. AWARDS BANQUET A banquet room can seat a times last year, how much is Benjamin’s rent each maximum of 69 people. The coach, principal, and month? vice principal have invited the award-winning girls’ tennis team to the banquet. If the tennis team consists of 22 girls, how many guests can each student bring? ANSWER: n = number of guests that each student can bring; ANSWER: 22n + 25 = 69; 2 guests x = the cost of rent each month; 622 + 428 + 240 + Solve each equation. Check your solution. 144 + 12x = 10,734; $775 per month 53. 60. BRIDGES The Sunshine Skyway Bridge spans ANSWER: Tampa Bay, Florida. Suppose one crew began –2 building south from St. Petersburg, and another crew began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg 54. approximately 5 years after construction began. a. Suppose the St. Petersburg crew built an average ANSWER: of 176 feet per month. Together the two crews built 3 21,120 feet of bridge. Determine the average number of feet built per month by the Bradenton crew. 55. b. About how many miles of bridge did each crew build? ANSWER: c. Is this answer reasonable? Explain. –4 ANSWER: 56. a. 176 ft b. 2 mi ANSWER: c. Yes; it seems reasonable that two crews working 3 4 miles apart would be able to complete the same amount of miles in the same amount of time. 57. 61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the ANSWER: number from zero. a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the 58. number line and their distance from zero. c. GRAPHICAL Make a graph of each integer x ANSWER: and its distance from zero y using the data points in the table.

d. VERBAL Make a conjecture about the integer and its distance from zero. Explain the reason for any changes in sign. 59. FINANCIAL LITERACY Benjamin spent $10,734 on his living expenses last year. Most of these ANSWER: expenses are listed at the right. Benjamin’s only a. other expense last year was rent. If he paid rent 12 times last year, how much is Benjamin’s rent each month? b.

ANSWER: x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month

60. BRIDGES The Sunshine Skyway Bridge spans Tampa Bay, Florida. Suppose one crew began building south from St. Petersburg, and another crew c. began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg approximately 5 years after construction began. a. Suppose the St. Petersburg crew built an average of 176 feet per month. Together the two crews built 21,120 feet of bridge. Determine the average number of feet built per month by the Bradenton crew. b. About how many miles of bridge did each crew build? c. Is this answer reasonable? Explain. d. For positive integers, the distance from zero is the ANSWER: same as the integer. For negative integers, the distance is the integer with the opposite sign because a. 176 ft distance is always positive. b. 2 mi c. Yes; it seems reasonable that two crews working 62. ERROR ANALYSIS Steven and Jade are solving 4 miles apart would be able to complete the same amount of miles in the same amount of time. for b2. Is either of them correct? Explain your reasoning. 61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the number from zero. a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the ANSWER: number line and their distance from zero. Sample answer: Jade; in the last step, when Steven c. GRAPHICAL Make a graph of each integer x subtracted b from each side, he mistakenly put the – and its distance from zero y using the data points in 1 the table. b1 in the numerator instead of after the entire d. VERBAL Make a conjecture about the integer fraction. and its distance from zero. Explain the reason for any changes in sign. 63. CHALLENGE Solve

ANSWER: for y1 a. ANSWER:

64. REASONING Use what you have learned in this lesson to explain why the following number trick works. • Take any number. • Multiply it by ten. • Subtract 30 from the result. • Divide the new result by 5. • Add 6 to the result. • Your new number is twice your original. ANSWER: Translating this number trick into an expression c. yields:

65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no d. For positive integers, the distance from zero is the solution and another example that has infinitely many same as the integer. For negative integers, the solutions. distance is the integer with the opposite sign because distance is always positive. ANSWER: Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2 62. ERROR ANALYSIS Steven and Jade are solving 66. WRITING IN MATH Compare and contrast the for b2. Is either of them correct? Substitution Property of Equality and the Transitive Explain your reasoning. Property of Equality. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property is done with two values, that is, one being substituted for another, the Transitive Property deals with three ANSWER: values, determining that since two values are equal to Sample answer: Jade; in the last step, when Steven a third value, then they must be equal. subtracted b1 from each side, he mistakenly put the – 67. The graph shows the solution of which inequality? b1 in the numerator instead of after the entire fraction.

63. CHALLENGE Solve

for y1 ANSWER:

A. C. 64. REASONING Use what you have learned in this lesson to explain why the following number trick B. D. works. • Take any number. ANSWER: • Multiply it by ten. D • Subtract 30 from the result. • Divide the new result by 5. • Add 6 to the result. 68. SAT/ACT What is subtracted from its • Your new number is twice your original. reciprocal? ANSWER: F Translating this number trick into an expression yields: G

K 65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no ANSWER: solution and another example that has infinitely many G solutions. 69. GEOMETRY Which of the following describes the ANSWER: transformation of to ? Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2

66. WRITING IN MATH Compare and contrast the Substitution Property of Equality and the Transitive Property of Equality. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property is done with two values, that is, one being substituted A. a reflection across the y-axis and a translation for another, the Transitive Property deals with three down 2 units values, determining that since two values are equal to B. a reflection across the x-axis and a translation a third value, then they must be equal. down 2 units 67. The graph shows the solution of which inequality? C. a rotation to the right and a translation down 2 units D. a rotation to the right and a translation right 2 units ANSWER: A

70. SHORT RESPONSE A local theater sold 1200 tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What A. C. was the percent decrease of tickets sold? ANSWER: B. D.

ANSWER: 71. Simplify . D ANSWER: 68. SAT/ACT What is subtracted from its –3x + 6y + 6z reciprocal? 72. BAKING Tamera is making two types of bread. F The first type of bread needs cups of flour, and

G the second needs cups of flour. Tamera wants to

H make 2 loaves of the first recipe and 3 loaves of the second recipe. How many cups of flour does she

J need? ANSWER: K

ANSWER: G 73. LANDMARKS Suppose the Space Needle in Seattle, Washington, casts a 220-foot shadow at the 69. GEOMETRY Which of the following describes the same time a nearby tourist casts a 2-foot shadow. If transformation of to ? the tourist is feet tall, how tall is the Space Needle?

A. a reflection across the y-axis and a translation down 2 units B. a reflection across the x-axis and a translation

down 2 units ANSWER: C. a rotation to the right and a translation down 605 ft 2 units D. a rotation to the right and a translation right 2 74. Evaluate , if a = 5, b = 7, and c = 2. units ANSWER: ANSWER: A 1

70. SHORT RESPONSE A local theater sold 1200 Identify the additive inverse for each number or tickets during the opening weekend of a movie. On expression.

the following weekend, 840 tickets were sold. What 75. was the percent decrease of tickets sold? ANSWER: ANSWER:

71. Simplify . ANSWER: 76. 3.5 –3x + 6y + 6z ANSWER: 72. BAKING Tamera is making two types of bread. The first type of bread needs cups of flour, and 77. ANSWER: the second needs cups of flour. Tamera wants to 2x make 2 loaves of the first recipe and 3 loaves of the second recipe. How many cups of flour does she 78.

need? ANSWER: ANSWER:

79. 73. LANDMARKS Suppose the Space Needle in ANSWER: Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If the tourist is feet tall, how tall is the Space Needle? 80. ANSWER: 1.25

81. ANSWER:

82.

ANSWER: ANSWER:

605 ft

74. Evaluate , if a = 5, b = 7, and c = 2.

ANSWER: 1 Identify the additive inverse for each number or expression.

75.

ANSWER:

76. 3.5 ANSWER:

77. ANSWER: 2x

78. ANSWER:

79.

ANSWER:

80. ANSWER: 1.25

81. ANSWER:

82. ANSWER:

Write an algebraic expression to represent each verbal expression. 1. the product of 12 and the sum of a number and negative 3 ANSWER:

2. the difference between the product of 4 and a number and the square of the number ANSWER: 2 4x – x

Write a verbal sentence to represent each equation. 3. ANSWER: The sum of five times a number and 7 equals 18.

4. ANSWER: The difference between the square of a number and 9 is 27.

5. ANSWER: The difference between five times a number and the cube of that number is 12.

ANSWER: Eight more than the quotient of a number and four is –16.

Name the property illustrated by each statement. 7.

ANSWER: Reflexive Property

8. If and , then . ANSWER: Write an algebraic expression to represent Transitive Property each verbal expression. Solve each equation. Check your solution. 1. the product of 12 and the sum of a number and 9. negative 3 ANSWER: ANSWER: 53

10. 2. the difference between the product of 4 and a number and the square of the number ANSWER: –6 ANSWER: 2 4x – x 11.

Write a verbal sentence to represent each ANSWER: equation. –8 3. ANSWER: 12. The sum of five times a number and 7 equals 18. ANSWER: –7 4. 13. ANSWER: The difference between the square of a number and ANSWER: 9 is 27. –6

5. 14. ANSWER: ANSWER: The difference between five times a number and the –4 cube of that number is 12. 15.

6. ANSWER: ANSWER: 3 Eight more than the quotient of a number and four is –16. 16.

Name the property illustrated by each ANSWER: statement. 8 7. 17. ANSWER: Reflexive Property ANSWER: 4 8. If and , then . 18. ANSWER: Transitive Property ANSWER:

Solve each equation. Check your solution. –5 9. Solve each equation or formula for the specified ANSWER: variable. 53 19. ,for q ANSWER: 10. ANSWER: –6 20. , for n 11. ANSWER: ANSWER: –8

12. 21. MULTIPLE CHOICE If , what is the ANSWER: –7 value of ? A –10

13. B –3 ANSWER: C 1 –6 D 5 ANSWER: 14. B ANSWER: Write an algebraic expression to represent –4 each verbal expression. 22. the difference between the product of four and a 15. number and 6 ANSWER: ANSWER: 3

16. 23. the product of the square of a number and 8 ANSWER: ANSWER: 8 8x2

17. 24. fifteen less than the cube of a number

ANSWER: ANSWER: 3 4 x – 15 25. five more than the quotient of a number and 4 18. ANSWER: ANSWER: –5

Solve each equation or formula for the specified Write a verbal sentence to represent each variable. equation. 19. ,for q 26. ANSWER: ANSWER: Four less than 8 times a number is 16.

27. 20. , for n ANSWER: ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

28. 21. MULTIPLE CHOICE If , what is the ANSWER:

value of ? Three less than four times the square of a number is 13. A –10 B –3 29. BASEBALL During a recent season, Miguel C 1 Cabrera and Mike Jacobs of the Florida Marlins hit a D 5 combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did ANSWER: each player hit? Define a variable, write an equation, B and solve the problem. ANSWER: Write an algebraic expression to represent each verbal expression. n = number of home runs Jacobs hit; n + 6 = number 22. the difference between the product of four and a of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 number and 6 home runs, Cabrera: 26 home runs. ANSWER: Name the property illustrated by each statement. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9

23. the product of the square of a number and 8 ANSWER: 30. Subtr. (=) ANSWER: 2 8x 31. If y = –3, then 7y = 7(–3) 24. fifteen less than the cube of a number ANSWER: Subst. ANSWER: 3 x – 15 32. If g = 3h and 3h = 16, then g = 16

25. five more than the quotient of a number and 4 ANSWER: Transitive Property ANSWER: 33. If –y = 13, then –(–y) = –13 ANSWER: Mult. (=) Write a verbal sentence to represent each equation. 34. MONEY Aiko and Kendra arrive at the state fair 26. with $32.50. What is the total number of rides they ANSWER: can go on if they each pay the entrance fee? Four less than 8 times a number is 16.

27.

ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

28. ANSWER: ANSWER: n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 Three less than four times the square of a number is 13. Solve each equation. Check your solution. 35. 29. BASEBALL During a recent season, Miguel Cabrera and Mike Jacobs of the Florida Marlins hit a ANSWER: combined total of 46 home runs. Cabrera hit 6 more 5 home runs than Jacobs. How many home runs did each player hit? Define a variable, write an equation, 36. and solve the problem. ANSWER: ANSWER: –7 n = number of home runs Jacobs hit; n + 6 = number of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 37. home runs, Cabrera: 26 home runs. ANSWER: Name the property illustrated by each –3 statement. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 38. ANSWER: ANSWER: 30. Subtr. (=) –5

31. If y = –3, then 7y = 7(–3) 39. 1-3 SolvingANSWER: Equations ANSWER: Subst. –6

32. If g = 3h and 3h = 16, then g = 16 40. ANSWER: ANSWER: Transitive Property 8 33. If –y = 13, then –(–y) = –13 ANSWER: 41. Mult. (=) ANSWER: 34. MONEY Aiko and Kendra arrive at the state fair –3 with $32.50. What is the total number of rides they can go on if they each pay the entrance fee? 42.

ANSWER: 4

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: s = length of a side; 5s = 100; 20 in.

ANSWER: 44. MEDICINE For Nina’s illness her doctor gives her n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 a prescription for 28 pills. The doctor says that she should take 4 pills the first day and then 2 pills each Solve each equation. Check your solution. day until her prescription runs out. For how many 35. days does she take 2 pills? ANSWER: ANSWER: 5 x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days

36. Solve each equation or formula for the specified variable. ANSWER: 45. , for m –7 ANSWER: 37. ANSWER: –3 46. , for a 38. ANSWER: ANSWER: –5

39. 47. , for h ANSWER: –6 ANSWER:

40. eSolutions Manual - Powered by Cognero Page 3 ANSWER: 48. , for y 8 ANSWER: 41.

ANSWER: 49. , for a –3 ANSWER: 42.

ANSWER: 50. , for z 4 ANSWER: 43. GEOMETRY The perimeter of a regular pentagon

is 100 inches. Find the length of each side. ANSWER: s = length of a side; 5s = 100; 20 in. 51. GEOMETRY The formula for the volume of a cylinder with radius r and height h is times the 44. MEDICINE For Nina’s illness her doctor gives her radius times the height. a prescription for 28 pills. The doctor says that she a. Write this as an algebraic expression. should take 4 pills the first day and then 2 pills each b. Solve the expression in part a for h. day until her prescription runs out. For how many days does she take 2 pills? ANSWER: ANSWER: a. b. x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days 52. AWARDS BANQUET A banquet room can seat a Solve each equation or formula for the specified maximum of 69 people. The coach, principal, and variable. vice principal have invited the award-winning girls’ 45. , for m tennis team to the banquet. If the tennis team consists of 22 girls, how many guests can each ANSWER: student bring?

ANSWER: n = number of guests that each student can bring; 22n + 25 = 69; 2 guests 46. , for a Solve each equation. Check your solution. ANSWER: 53. ANSWER: –2 47. , for h

ANSWER: 54.

ANSWER: 3 48. , for y 55.

ANSWER: ANSWER: –4

49. , for a 56. ANSWER: ANSWER: 3

57. 50. , for z ANSWER: ANSWER:

54. approximately 5 years after construction began. a. Suppose the St. Petersburg crew built an average of 176 feet per month. Together the two crews built ANSWER: 21,120 feet of bridge. Determine the average number 3 of feet built per month by the Bradenton crew. b. About how many miles of bridge did each crew 55. build? ANSWER: c. Is this answer reasonable? Explain. –4 ANSWER: a. 176 ft 56. b. 2 mi ANSWER: c. Yes; it seems reasonable that two crews working 3 4 miles apart would be able to complete the same amount of miles in the same amount of time.

57. 61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the ANSWER: number from zero. a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the number line and their distance from zero. 58. c. GRAPHICAL Make a graph of each integer x and its distance from zero y using the data points in ANSWER: the table. d. VERBAL Make a conjecture about the integer and its distance from zero. Explain the reason for any changes in sign. 59. FINANCIAL LITERACY Benjamin spent $10,734 on his living expenses last year. Most of these ANSWER: expenses are listed at the right. Benjamin’s only a. other expense last year was rent. If he paid rent 12 times last year, how much is Benjamin’s rent each month? b.

ANSWER: x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month

60. BRIDGES The Sunshine Skyway Bridge spans Tampa Bay, Florida. Suppose one crew began building south from St. Petersburg, and another crew c. began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg approximately 5 years after construction began. a. Suppose the St. Petersburg crew built an average of 176 feet per month. Together the two crews built 21,120 feet of bridge. Determine the average number of feet built per month by the Bradenton crew. b. About how many miles of bridge did each crew build? c. Is this answer reasonable? Explain. d. For positive integers, the distance from zero is the same as the integer. For negative integers, the ANSWER: distance is the integer with the opposite sign because a. 176 ft distance is always positive. b. 2 mi c. Yes; it seems reasonable that two crews working 62. ERROR ANALYSIS Steven and Jade are solving 4 miles apart would be able to complete the same for b . Is either of them correct? amount of miles in the same amount of time. 2 Explain your reasoning. 61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the number from zero. a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the ANSWER: number line and their distance from zero. Sample answer: Jade; in the last step, when Steven c. GRAPHICAL Make a graph of each integer x subtracted b1 from each side, he mistakenly put the – and its distance from zero y using the data points in the table. b1 in the numerator instead of after the entire d. VERBAL Make a conjecture about the integer fraction. and its distance from zero. Explain the reason for any changes in sign. 63. CHALLENGE Solve

ANSWER: for y1 a. ANSWER:

65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no d. For positive integers, the distance from zero is the solution and another example that has infinitely many same as the integer. For negative integers, the solutions. distance is the integer with the opposite sign because distance is always positive. ANSWER: Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2 62. ERROR ANALYSIS Steven and Jade are solving 66. WRITING IN MATH Compare and contrast the for b2. Is either of them correct? Substitution Property of Equality and the Transitive Property of Equality. Explain your reasoning. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property is done with two values, that is, one being substituted for another, the Transitive Property deals with three ANSWER: values, determining that since two values are equal to Sample answer: Jade; in the last step, when Steven a third value, then they must be equal. subtracted b from each side, he mistakenly put the – 1 67. The graph shows the solution of which inequality? b1 in the numerator instead of after the entire fraction.

63. CHALLENGE Solve

for y1 ANSWER:

A. C. 64. REASONING Use what you have learned in this

lesson to explain why the following number trick B. D. works. • Take any number. ANSWER: • Multiply it by ten. D • Subtract 30 from the result. • Divide the new result by 5. 68. SAT/ACT What is subtracted from its • Add 6 to the result. • Your new number is twice your original. reciprocal? F ANSWER: Translating this number trick into an expression yields: G

65. OPEN ENDED Provide one example of an equation ANSWER: involving the Distributive Property that has no G solution and another example that has infinitely many solutions. 69. GEOMETRY Which of the following describes the ANSWER: transformation of to ? Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2

66. WRITING IN MATH Compare and contrast the Substitution Property of Equality and the Transitive Property of Equality. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property is done with two values, that is, one being substituted A. a reflection across the y-axis and a translation for another, the Transitive Property deals with three down 2 units values, determining that since two values are equal to B. a reflection across the x-axis and a translation a third value, then they must be equal. down 2 units C. a rotation to the right and a translation down 67. The graph shows the solution of which inequality? 2 units D. a rotation to the right and a translation right 2 units ANSWER: A

70. SHORT RESPONSE A local theater sold 1200 tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What

A. C. was the percent decrease of tickets sold? ANSWER: B. D.

ANSWER: 71. Simplify . D ANSWER: –3x + 6y + 6z 68. SAT/ACT What is subtracted from its reciprocal? 72. BAKING Tamera is making two types of bread. F The first type of bread needs cups of flour, and

G the second needs cups of flour. Tamera wants to

H make 2 loaves of the first recipe and 3 loaves of the second recipe. How many cups of flour does she need? J ANSWER:

A. a reflection across the y-axis and a translation down 2 units B. a reflection across the x-axis and a translation down 2 units ANSWER: C. a rotation to the right and a translation down 605 ft 2 units D. a rotation to the right and a translation right 2 74. Evaluate , if a = 5, b = 7, and c = 2. units ANSWER: ANSWER: 1 A Identify the additive inverse for each number or 70. SHORT RESPONSE A local theater sold 1200 expression. tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What 75. was the percent decrease of tickets sold? ANSWER: ANSWER:

71. Simplify . ANSWER: 76. 3.5 –3x + 6y + 6z ANSWER:

72. BAKING Tamera is making two types of bread.

The first type of bread needs cups of flour, and 77. ANSWER: the second needs cups of flour. Tamera wants to 2x

make 2 loaves of the first recipe and 3 loaves of the 78. second recipe. How many cups of flour does she need? ANSWER: ANSWER:

79.

73. LANDMARKS Suppose the Space Needle in ANSWER: Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If the tourist is feet tall, how tall is the Space 80. Needle? ANSWER: 1.25

81. ANSWER:

82.

ANSWER: ANSWER: 605 ft

74. Evaluate , if a = 5, b = 7, and c = 2.

ANSWER: 1 Identify the additive inverse for each number or expression.

75.

ANSWER:

76. 3.5 ANSWER:

77. ANSWER: 2x

78. ANSWER:

79.

ANSWER:

80. ANSWER: 1.25

81. ANSWER:

82. ANSWER:

Write an algebraic expression to represent each verbal expression. 1. the product of 12 and the sum of a number and negative 3 ANSWER:

2. the difference between the product of 4 and a number and the square of the number ANSWER: 2 4x – x

Write a verbal sentence to represent each equation. 3. ANSWER: The sum of five times a number and 7 equals 18.

4. ANSWER: The difference between the square of a number and 9 is 27.

5. ANSWER: The difference between five times a number and the cube of that number is 12.

ANSWER: Eight more than the quotient of a number and four is –16.

Name the property illustrated by each statement. 7.

ANSWER: Reflexive Property

8. If and , then . ANSWER: Transitive Property

Write an algebraic expression to represent Solve each equation. Check your solution. each verbal expression. 9. 1. the product of 12 and the sum of a number and negative 3 ANSWER: 53 ANSWER:

10. ANSWER: 2. the difference between the product of 4 and a number and the square of the number –6

ANSWER: 11. 2 4x – x ANSWER: Write a verbal sentence to represent each –8 equation. 3. 12. ANSWER: ANSWER: The sum of five times a number and 7 equals 18. –7

4. 13. ANSWER: ANSWER: The difference between the square of a number and –6 9 is 27. 14. 5. ANSWER: ANSWER: –4 The difference between five times a number and the cube of that number is 12. 15.

ANSWER: 6. 3 ANSWER: Eight more than the quotient of a number and four is 16. –16. ANSWER: Name the property illustrated by each 8 statement. 7. 17.

ANSWER: ANSWER: Reflexive Property 4

8. If and , then . 18. ANSWER: ANSWER: Transitive Property –5

Solve each equation. Check your solution. Solve each equation or formula for the specified 9. variable. ANSWER: 19. ,for q 53 ANSWER:

10. ANSWER: –6 20. , for n ANSWER: 11.

ANSWER: –8 21. MULTIPLE CHOICE If , what is the 12.

ANSWER: –5 Write a verbal sentence to represent each Solve each equation or formula for the specified equation. variable. 26. 19. ,for q ANSWER: ANSWER: Four less than 8 times a number is 16.

27.

20. , for n ANSWER: ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

28.

21. MULTIPLE CHOICE If , what is the ANSWER: Three less than four times the square of a number is

ANSWER: 23. the product of the square of a number and 8 30. Subtr. (=) ANSWER: 31. If y = –3, then 7y = 7(–3) 8x2 ANSWER: 24. fifteen less than the cube of a number Subst. ANSWER: 32. If g = 3h and 3h = 16, then g = 16 3 x – 15 ANSWER: 25. five more than the quotient of a number and 4 Transitive Property ANSWER: 33. If –y = 13, then –(–y) = –13 ANSWER: Mult. (=)

27.

ANSWER: The quotient of the sum of 3 and a number and 4 is 5. ANSWER: 28. n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 ANSWER: Solve each equation. Check your solution. Three less than four times the square of a number is 13. 35. ANSWER: 29. BASEBALL During a recent season, Miguel Cabrera and Mike Jacobs of the Florida Marlins hit a 5 combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did 36. each player hit? Define a variable, write an equation, and solve the problem. ANSWER: –7 ANSWER: n = number of home runs Jacobs hit; n + 6 = number 37. of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 home runs, Cabrera: 26 home runs. ANSWER: –3 Name the property illustrated by each statement. 38. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 ANSWER: ANSWER: –5 30. Subtr. (=) 39. 31. If y = –3, then 7y = 7(–3) ANSWER: ANSWER: –6 Subst. 40. 32. If g = 3h and 3h = 16, then g = 16 ANSWER: ANSWER: 8 Transitive Property

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: s = length of a side; 5s = 100; 20 in.

44. MEDICINE For Nina’s illness her doctor gives her ANSWER: a prescription for 28 pills. The doctor says that she should take 4 pills the first day and then 2 pills each n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 day until her prescription runs out. For how many Solve each equation. Check your solution. days does she take 2 pills? 35. ANSWER: ANSWER: x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days 5 Solve each equation or formula for the specified 36. variable. 45. , for m ANSWER: –7 ANSWER:

37. ANSWER: –3 46. , for a

38. ANSWER: ANSWER: –5

39. 47. , for h

ANSWER: ANSWER: –6

40. 48. , for y ANSWER: 8 ANSWER:

41. 49. , for a ANSWER: –3 ANSWER:

42. 50. , for z ANSWER: 4 ANSWER:

46. , for a Solve each equation. Check your solution. 53. ANSWER: ANSWER: 1-3 Solving Equations –2

47. , for h 54. ANSWER: ANSWER: 3

55. 48. , for y ANSWER: ANSWER: –4

56. 49. , for a ANSWER: ANSWER: 3

57.

50. , for z ANSWER:

ANSWER:

Solve each equation. Check your solution. 60. BRIDGES The Sunshine Skyway Bridge spans 53. Tampa Bay, Florida. Suppose one crew began ANSWER: building south from St. Petersburg, and another crew began building north from Bradenton. The two crews –2 met 10,560 feet south of St. Petersburg approximately 5 years after construction began. eSolutions Manual - Powered by Cognero a. Suppose the St. Petersburg crew built an averagePage 4 54. of 176 feet per month. Together the two crews built 21,120 feet of bridge. Determine the average number ANSWER: of feet built per month by the Bradenton crew. 3 b. About how many miles of bridge did each crew build? 55. c. Is this answer reasonable? Explain. ANSWER: ANSWER: –4 a. 176 ft b. 2 mi 56. c. Yes; it seems reasonable that two crews working ANSWER: 4 miles apart would be able to complete the same 3 amount of miles in the same amount of time. 61. MULTIPLE REPRESENTATIONS The absolute 57. value of a number describes the distance of the number from zero. ANSWER: a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the number line and their distance from zero. c. GRAPHICAL Make a graph of each integer x 58. and its distance from zero y using the data points in the table. ANSWER: d. VERBAL Make a conjecture about the integer and its distance from zero. Explain the reason for any changes in sign. ANSWER: 59. FINANCIAL LITERACY Benjamin spent $10,734 on his living expenses last year. Most of these a. expenses are listed at the right. Benjamin’s only other expense last year was rent. If he paid rent 12 b. times last year, how much is Benjamin’s rent each month?

ANSWER: x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month

61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the number from zero.

a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. ANSWER: b. TABULAR Create a table of the integers on the Sample answer: Jade; in the last step, when Steven

number line and their distance from zero. subtracted b1 from each side, he mistakenly put the – c. GRAPHICAL Make a graph of each integer x b in the numerator instead of after the entire and its distance from zero y using the data points in 1 the table. fraction. d. VERBAL Make a conjecture about the integer CHALLENGE and its distance from zero. Explain the reason for any 63. Solve changes in sign. for y1 ANSWER: ANSWER: a.

62. ERROR ANALYSIS Steven and Jade are solving 66. WRITING IN MATH Compare and contrast the Substitution Property of Equality and the Transitive for b2. Is either of them correct? Property of Equality. Explain your reasoning. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property is done with two values, that is, one being substituted for another, the Transitive Property deals with three values, determining that since two values are equal to ANSWER: a third value, then they must be equal. Sample answer: Jade; in the last step, when Steven 67. The graph shows the solution of which inequality? subtracted b1 from each side, he mistakenly put the –

b1 in the numerator instead of after the entire fraction.

63. CHALLENGE Solve

for y1

ANSWER:

A. C.

ANSWER: 65. OPEN ENDED Provide one example of an equation G involving the Distributive Property that has no solution and another example that has infinitely many 69. GEOMETRY Which of the following describes the solutions. transformation of to ? ANSWER: Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2

70. SHORT RESPONSE A local theater sold 1200 tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What was the percent decrease of tickets sold?

A. C. ANSWER:

B. D. 71. Simplify . ANSWER: ANSWER: D –3x + 6y + 6z

J ANSWER:

ANSWER: 73. LANDMARKS Suppose the Space Needle in Seattle, Washington, casts a 220-foot shadow at the G same time a nearby tourist casts a 2-foot shadow. If 69. GEOMETRY Which of the following describes the the tourist is feet tall, how tall is the Space transformation of to ? Needle?

71. Simplify . 76. 3.5 ANSWER: ANSWER: –3x + 6y + 6z

79.

81. ANSWER:

82. ANSWER:

ANSWER: 605 ft

74. Evaluate , if a = 5, b = 7, and c = 2.

ANSWER: 1 Identify the additive inverse for each number or expression.

75.

ANSWER:

76. 3.5 ANSWER:

77. ANSWER: 2x

78. ANSWER:

79.

ANSWER:

80. ANSWER: 1.25

81. ANSWER:

82. ANSWER:

Write an algebraic expression to represent each verbal expression. 1. the product of 12 and the sum of a number and negative 3 ANSWER:

2. the difference between the product of 4 and a number and the square of the number ANSWER: 2 4x – x

Write a verbal sentence to represent each equation. 3. ANSWER: The sum of five times a number and 7 equals 18.

Write an algebraic expression to represent each verbal expression. 4. 1. the product of 12 and the sum of a number and ANSWER: negative 3 The difference between the square of a number and ANSWER: 9 is 27.

2. the difference between the product of 4 and a ANSWER: number and the square of the number The difference between five times a number and the cube of that number is 12. ANSWER: 2 4x – x 6. Write a verbal sentence to represent each equation. ANSWER: 3. Eight more than the quotient of a number and four is –16. ANSWER: The sum of five times a number and 7 equals 18. Name the property illustrated by each statement. 7. 4. ANSWER: ANSWER: Reflexive Property The difference between the square of a number and 9 is 27. 8. If and , then . 5. ANSWER: ANSWER: Transitive Property The difference between five times a number and the cube of that number is 12. Solve each equation. Check your solution. 9.

6. ANSWER: 53 ANSWER: Eight more than the quotient of a number and four is 10. –16. ANSWER: Name the property illustrated by each –6 statement. 7. 11. ANSWER: ANSWER: Reflexive Property –8

8. If and , then . 12. ANSWER: ANSWER: Transitive Property –7

Solve each equation. Check your solution. 13. 9. ANSWER: ANSWER: –6 53 14. 10. ANSWER: ANSWER: –4 –6 15. 11. ANSWER: ANSWER: 3 –8 16. 12. ANSWER: ANSWER: 8 –7

13. 17. ANSWER: ANSWER: –6 4

14. 18. ANSWER: ANSWER: –4 –5

15. Solve each equation or formula for the specified variable. ANSWER: 19. ,for q 3 ANSWER:

16.

ANSWER: 8 20. , for n ANSWER: 17.

ANSWER: 4 21. MULTIPLE CHOICE If , what is the 18.

ANSWER: value of ? –5 A –10 B –3 Solve each equation or formula for the specified C 1 variable. D 5 19. ,for q ANSWER: ANSWER: B

Write an algebraic expression to represent each verbal expression. 22. the difference between the product of four and a 20. , for n number and 6 ANSWER: ANSWER:

23. the product of the square of a number and 8 21. MULTIPLE CHOICE If , what is the ANSWER:

value of ? 8x2

A –10 24. fifteen less than the cube of a number B –3 ANSWER: C 1 3 D 5 x – 15 ANSWER: 25. five more than the quotient of a number and 4

B ANSWER: Write an algebraic expression to represent each verbal expression. 22. the difference between the product of four and a number and 6 Write a verbal sentence to represent each equation. ANSWER: 26.

ANSWER: Four less than 8 times a number is 16. 23. the product of the square of a number and 8 ANSWER: 27. 8x2

24. fifteen less than the cube of a number ANSWER: The quotient of the sum of 3 and a number and 4 is ANSWER: 5. 3 x – 15 28. 25. five more than the quotient of a number and 4 ANSWER: ANSWER: Three less than four times the square of a number is 13.

29. BASEBALL During a recent season, Miguel Write a verbal sentence to represent each Cabrera and Mike Jacobs of the Florida Marlins hit a equation. combined total of 46 home runs. Cabrera hit 6 more 26. home runs than Jacobs. How many home runs did each player hit? Define a variable, write an equation, ANSWER: and solve the problem. Four less than 8 times a number is 16. ANSWER: n = number of home runs Jacobs hit; n + 6 = number

27. of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 home runs, Cabrera: 26 home runs.

ANSWER: Name the property illustrated by each The quotient of the sum of 3 and a number and 4 is statement. 5. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9

28. ANSWER: 30. Subtr. (=) ANSWER: Three less than four times the square of a number is 31. If y = –3, then 7y = 7(–3) 13. ANSWER: 29. BASEBALL During a recent season, Miguel Subst. Cabrera and Mike Jacobs of the Florida Marlins hit a combined total of 46 home runs. Cabrera hit 6 more 32. If g = 3h and 3h = 16, then g = 16 home runs than Jacobs. How many home runs did each player hit? Define a variable, write an equation, ANSWER: and solve the problem. Transitive Property ANSWER: 33. If –y = 13, then –(–y) = –13 n = number of home runs Jacobs hit; n + 6 = number ANSWER: of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 Mult. (=) home runs, Cabrera: 26 home runs.

Name the property illustrated by each 34. MONEY Aiko and Kendra arrive at the state fair statement. with $32.50. What is the total number of rides they 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 can go on if they each pay the entrance fee? ANSWER: 30. Subtr. (=)

31. If y = –3, then 7y = 7(–3) ANSWER: Subst. 32. If g = 3h and 3h = 16, then g = 16 ANSWER: ANSWER: Transitive Property n = number of rides; 2(7.50) + n(2.50) = 32.50; 7

33. If –y = 13, then –(–y) = –13 Solve each equation. Check your solution. 35. ANSWER: Mult. (=) ANSWER: 5 34. MONEY Aiko and Kendra arrive at the state fair with $32.50. What is the total number of rides they can go on if they each pay the entrance fee? 36. ANSWER: –7

37. ANSWER: –3

38.

ANSWER: ANSWER: –5 n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 39. Solve each equation. Check your solution. 35. ANSWER: ANSWER: –6 5 40.

36. ANSWER: 8 ANSWER: –7 41. 37. ANSWER: ANSWER: –3 –3

38. 42.

ANSWER: ANSWER: –5 4

39. 43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: –6 ANSWER: s = length of a side; 5s = 100; 20 in. 40. 44. MEDICINE For Nina’s illness her doctor gives her ANSWER: a prescription for 28 pills. The doctor says that she 8 should take 4 pills the first day and then 2 pills each day until her prescription runs out. For how many

41. days does she take 2 pills? ANSWER: ANSWER: x = the number of days she takes 2 pills; 4 + 2x = 28; –3 12 days

Solve each equation or formula for the specified 42. variable. 45. , for m ANSWER: 4 ANSWER:

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: 46. , for a s = length of a side; 5s = 100; 20 in. ANSWER: 44. MEDICINE For Nina’s illness her doctor gives her a prescription for 28 pills. The doctor says that she should take 4 pills the first day and then 2 pills each day until her prescription runs out. For how many

days does she take 2 pills? 47. , for h ANSWER: ANSWER: x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days

Solve each equation or formula for the specified 48. , for y variable. 45. , for m ANSWER: ANSWER:

49. , for a ANSWER: 46. , for a

ANSWER: 50. , for z ANSWER: 47. , for h ANSWER: 51. GEOMETRY The formula for the volume of a cylinder with radius r and height h is times the radius times the height. 48. , for y a. Write this as an algebraic expression. b. Solve the expression in part a for h. ANSWER: ANSWER: a. b. 49. , for a

ANSWER: 52. AWARDS BANQUET A banquet room can seat a maximum of 69 people. The coach, principal, and vice principal have invited the award-winning girls’ tennis team to the banquet. If the tennis team 50. , for z consists of 22 girls, how many guests can each student bring? ANSWER: ANSWER: n = number of guests that each student can bring; 22n + 25 = 69; 2 guests

51. GEOMETRY The formula for the volume of a Solve each equation. Check your solution. cylinder with radius r and height h is times the 53. radius times the height. a. Write this as an algebraic expression. ANSWER: b. Solve the expression in part a for h. –2 ANSWER:

a. 54. b. ANSWER: 3 52. AWARDS BANQUET A banquet room can seat a maximum of 69 people. The coach, principal, and 55. vice principal have invited the award-winning girls’ tennis team to the banquet. If the tennis team ANSWER: consists of 22 girls, how many guests can each –4 student bring? ANSWER: 56. n = number of guests that each student can bring; ANSWER: 22n + 25 = 69; 2 guests 3 Solve each equation. Check your solution. 53. 57. ANSWER: –2 ANSWER:

54. 58. ANSWER: 3 ANSWER:

55.

ANSWER: –4 59. FINANCIAL LITERACY Benjamin spent $10,734 on his living expenses last year. Most of these 56. expenses are listed at the right. Benjamin’s only other expense last year was rent. If he paid rent 12 ANSWER: times last year, how much is Benjamin’s rent each 3 month?

57.

ANSWER:

ANSWER: x = the cost of rent each month; 622 + 428 + 240 + 58. 144 + 12x = 10,734; $775 per month

ANSWER: 60. BRIDGES The Sunshine Skyway Bridge spans Tampa Bay, Florida. Suppose one crew began building south from St. Petersburg, and another crew began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg 59. FINANCIAL LITERACY Benjamin spent $10,734 approximately 5 years after construction began. on his living expenses last year. Most of these a. Suppose the St. Petersburg crew built an average expenses are listed at the right. Benjamin’s only of 176 feet per month. Together the two crews built other expense last year was rent. If he paid rent 12 21,120 feet of bridge. Determine the average number times last year, how much is Benjamin’s rent each of feet built per month by the Bradenton crew. month? b. About how many miles of bridge did each crew build? c. Is this answer reasonable? Explain. ANSWER: a. 176 ft

b. 2 mi ANSWER: c. Yes; it seems reasonable that two crews working 1-3 Solvingx = the cost Equations of rent each month; 622 + 428 + 240 + 4 miles apart would be able to complete the same 144 + 12x = 10,734; $775 per month amount of miles in the same amount of time.

60. BRIDGES The Sunshine Skyway Bridge spans 61. MULTIPLE REPRESENTATIONS The absolute Tampa Bay, Florida. Suppose one crew began value of a number describes the distance of the building south from St. Petersburg, and another crew number from zero. began building north from Bradenton. The two crews a. GEOMETRIC Draw a number line. Label the met 10,560 feet south of St. Petersburg integers from –5 to 5. approximately 5 years after construction began. b. TABULAR Create a table of the integers on the a. Suppose the St. Petersburg crew built an average number line and their distance from zero. of 176 feet per month. Together the two crews built c. GRAPHICAL Make a graph of each integer x 21,120 feet of bridge. Determine the average number and its distance from zero y using the data points in of feet built per month by the Bradenton crew. the table. b. About how many miles of bridge did each crew d. VERBAL Make a conjecture about the integer build? and its distance from zero. Explain the reason for any c. Is this answer reasonable? Explain. changes in sign. ANSWER: ANSWER: a. 176 ft a. b. 2 mi c. Yes; it seems reasonable that two crews working 4 miles apart would be able to complete the same b. amount of miles in the same amount of time.

61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the number from zero. a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the number line and their distance from zero. c. GRAPHICAL Make a graph of each integer x and its distance from zero y using the data points in the table.

d. VERBAL Make a conjecture about the integer c. and its distance from zero. Explain the reason for any changes in sign. ANSWER: a.

d. For positive integers, the distance from zero is the same as the integer. For negative integers, the distance is the integer with the opposite sign because distance is always positive.

62. ERROR ANALYSIS Steven and Jade are solving

for b2. Is either of them correct? Explain your reasoning. eSolutions Manual - Powered by Cognero Page 5 c.

ANSWER: Sample answer: Jade; in the last step, when Steven subtracted b1 from each side, he mistakenly put the –

b1 in the numerator instead of after the entire fraction.

d. For positive integers, the distance from zero is the 63. CHALLENGE Solve same as the integer. For negative integers, the distance is the integer with the opposite sign because for y1 distance is always positive. ANSWER: 62. ERROR ANALYSIS Steven and Jade are solving

for b2. Is either of them correct? 64. REASONING Use what you have learned in this Explain your reasoning. lesson to explain why the following number trick works. • Take any number. • Multiply it by ten. • Subtract 30 from the result. • Divide the new result by 5. ANSWER: • Add 6 to the result. Sample answer: Jade; in the last step, when Steven • Your new number is twice your original. subtracted b1 from each side, he mistakenly put the – ANSWER: b1 in the numerator instead of after the entire Translating this number trick into an expression fraction. yields: 63. CHALLENGE Solve

for y1 ANSWER:

65. OPEN ENDED Provide one example of an equation REASONING 64. Use what you have learned in this involving the Distributive Property that has no lesson to explain why the following number trick solution and another example that has infinitely many

works. solutions. • Take any number. • Multiply it by ten. ANSWER: • Subtract 30 from the result. Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2 • Divide the new result by 5. 66. WRITING IN MATH Compare and contrast the • Add 6 to the result. Substitution Property of Equality and the Transitive • Your new number is twice your original. Property of Equality. ANSWER: ANSWER: Translating this number trick into an expression Sample answer: The Transitive Property utilizes the

yields: Substitution Property. While the Substitution Property is done with two values, that is, one being substituted for another, the Transitive Property deals with three values, determining that since two values are equal to a third value, then they must be equal.

67. The graph shows the solution of which inequality?

65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no solution and another example that has infinitely many solutions. ANSWER: Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2

66. WRITING IN MATH Compare and contrast the Substitution Property of Equality and the Transitive A. C. Property of Equality. B. D. ANSWER: Sample answer: The Transitive Property utilizes the ANSWER: Substitution Property. While the Substitution Property D is done with two values, that is, one being substituted for another, the Transitive Property deals with three values, determining that since two values are equal to 68. SAT/ACT What is subtracted from its a third value, then they must be equal. reciprocal? 67. The graph shows the solution of which inequality? F

A. C. ANSWER:

B. D. G 69. GEOMETRY Which of the following describes the ANSWER: transformation of to ? D

68. SAT/ACT What is subtracted from its reciprocal? F

A. H a reflection across the y-axis and a translation down 2 units B. a reflection across the x-axis and a translation J down 2 units C. a rotation to the right and a translation down K 2 units D. a rotation to the right and a translation right 2 ANSWER: units G ANSWER: 69. GEOMETRY Which of the following describes the A transformation of to ? 70. SHORT RESPONSE A local theater sold 1200 tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What was the percent decrease of tickets sold? ANSWER:

71. Simplify .

A. a reflection across the y-axis and a translation ANSWER: down 2 units –3x + 6y + 6z B. a reflection across the x-axis and a translation down 2 units 72. BAKING Tamera is making two types of bread. C. a rotation to the right and a translation down 2 units The first type of bread needs cups of flour, and D. a rotation to the right and a translation right 2 units the second needs cups of flour. Tamera wants to ANSWER: make 2 loaves of the first recipe and 3 loaves of the A second recipe. How many cups of flour does she need? SHORT RESPONSE 70. A local theater sold 1200 ANSWER: tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What was the percent decrease of tickets sold?

ANSWER: 73. LANDMARKS Suppose the Space Needle in Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If 71. Simplify . the tourist is feet tall, how tall is the Space ANSWER: Needle? –3x + 6y + 6z

72. BAKING Tamera is making two types of bread. The first type of bread needs cups of flour, and

the second needs cups of flour. Tamera wants to make 2 loaves of the first recipe and 3 loaves of the second recipe. How many cups of flour does she need? ANSWER: ANSWER: 605 ft 74. Evaluate , if a = 5, b = 7, and c = 2.

73. LANDMARKS Suppose the Space Needle in ANSWER: Seattle, Washington, casts a 220-foot shadow at the 1 same time a nearby tourist casts a 2-foot shadow. If the tourist is feet tall, how tall is the Space Identify the additive inverse for each number or expression. Needle? 75.

ANSWER:

76. 3.5

ANSWER:

ANSWER: 605 ft 77.

74. Evaluate , if a = 5, b = 7, and c = 2. ANSWER: 2x ANSWER: 1 78. Identify the additive inverse for each number or ANSWER: expression.

75. 79. ANSWER: ANSWER:

76. 3.5 80. ANSWER: ANSWER: 1.25

77. 81. ANSWER: ANSWER: 2x

78. 82. ANSWER: ANSWER:

79.

ANSWER:

80. ANSWER: 1.25

81. ANSWER:

82. ANSWER:

Write an algebraic expression to represent each verbal expression. 1. the product of 12 and the sum of a number and negative 3 ANSWER:

2. the difference between the product of 4 and a number and the square of the number ANSWER: 2 4x – x

Write a verbal sentence to represent each equation. 3. ANSWER: The sum of five times a number and 7 equals 18.

4. ANSWER: The difference between the square of a number and 9 is 27.

5. ANSWER: The difference between five times a number and the cube of that number is 12.

ANSWER: Eight more than the quotient of a number and four is –16.

Name the property illustrated by each statement. 7.

ANSWER: Reflexive Property

8. If and , then . ANSWER: Transitive Property Write an algebraic expression to represent each verbal expression. Solve each equation. Check your solution. 1. the product of 12 and the sum of a number and 9. negative 3 ANSWER: ANSWER: 53

10.

2. the difference between the product of 4 and a ANSWER: number and the square of the number –6 ANSWER: 2 11. 4x – x ANSWER: Write a verbal sentence to represent each –8 equation.

3. 12. ANSWER: ANSWER: The sum of five times a number and 7 equals 18. –7

4. 13. ANSWER: ANSWER: The difference between the square of a number and –6 9 is 27. 14. 5. ANSWER: ANSWER: –4 The difference between five times a number and the cube of that number is 12. 15.

6. ANSWER: 3 ANSWER: Eight more than the quotient of a number and four is 16. –16. ANSWER: Name the property illustrated by each 8 statement. 7. 17.

ANSWER: ANSWER: Reflexive Property 4

8. If and , then . 18.

ANSWER: ANSWER: Transitive Property –5 Solve each equation. Check your solution. 9. Solve each equation or formula for the specified variable. ANSWER: 19. ,for q 53 ANSWER:

10. ANSWER: –6 20. , for n

11. ANSWER:

ANSWER: –8 21. MULTIPLE CHOICE If , what is the 12.

ANSWER: value of ? –7 A –10 B 13. –3 C 1 ANSWER: D 5 –6 ANSWER: 14. B ANSWER: Write an algebraic expression to represent –4 each verbal expression. 22. the difference between the product of four and a number and 6 15. ANSWER: ANSWER: 3 23. the product of the square of a number and 8 16. ANSWER: ANSWER: 8x2 8 24. fifteen less than the cube of a number 17. ANSWER: 3 ANSWER: x – 15 4 25. five more than the quotient of a number and 4 18. ANSWER: ANSWER: –5 Write a verbal sentence to represent each Solve each equation or formula for the specified equation. variable. 26. 19. ,for q ANSWER: ANSWER: Four less than 8 times a number is 16.

27. 20. , for n ANSWER: ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

28. 21. MULTIPLE CHOICE If , what is the ANSWER: Three less than four times the square of a number is value of ? 13.

A –10 29. BASEBALL During a recent season, Miguel B –3 Cabrera and Mike Jacobs of the Florida Marlins hit a C 1 combined total of 46 home runs. Cabrera hit 6 more D 5 home runs than Jacobs. How many home runs did each player hit? Define a variable, write an equation, ANSWER: and solve the problem. B ANSWER: Write an algebraic expression to represent n = number of home runs Jacobs hit; n + 6 = number each verbal expression. of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 22. the difference between the product of four and a home runs, Cabrera: 26 home runs. number and 6 Name the property illustrated by each ANSWER: statement. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 ANSWER: 23. the product of the square of a number and 8 30. Subtr. (=) ANSWER: 31. If y = –3, then 7y = 7(–3) 8x2 ANSWER: 24. fifteen less than the cube of a number Subst. ANSWER: 32. If g = 3h and 3h = 16, then g = 16 3 x – 15 ANSWER: 25. five more than the quotient of a number and 4 Transitive Property ANSWER: 33. If –y = 13, then –(–y) = –13

ANSWER: Mult. (=) Write a verbal sentence to represent each MONEY equation. 34. Aiko and Kendra arrive at the state fair with $32.50. What is the total number of rides they 26. can go on if they each pay the entrance fee? ANSWER: Four less than 8 times a number is 16.

27.

ANSWER: The quotient of the sum of 3 and a number and 4 is 5. 28. ANSWER: n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 ANSWER: Three less than four times the square of a number is Solve each equation. Check your solution. 13. 35.

29. BASEBALL During a recent season, Miguel ANSWER: Cabrera and Mike Jacobs of the Florida Marlins hit a 5 combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did 36. each player hit? Define a variable, write an equation, and solve the problem. ANSWER: ANSWER: –7 n = number of home runs Jacobs hit; n + 6 = number 37. of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 home runs, Cabrera: 26 home runs. ANSWER: –3 Name the property illustrated by each statement. 38. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 ANSWER: ANSWER: –5 30. Subtr. (=) 39. 31. If y = –3, then 7y = 7(–3) ANSWER: ANSWER: –6 Subst. 40. 32. If g = 3h and 3h = 16, then g = 16 ANSWER: ANSWER: Transitive Property 8

33. If –y = 13, then –(–y) = –13 41. ANSWER: Mult. (=) ANSWER: –3 34. MONEY Aiko and Kendra arrive at the state fair with $32.50. What is the total number of rides they 42. can go on if they each pay the entrance fee? ANSWER: 4

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: s = length of a side; 5s = 100; 20 in.

44. MEDICINE For Nina’s illness her doctor gives her ANSWER: a prescription for 28 pills. The doctor says that she n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 should take 4 pills the first day and then 2 pills each day until her prescription runs out. For how many Solve each equation. Check your solution. days does she take 2 pills? 35. ANSWER: ANSWER: x = the number of days she takes 2 pills; 4 + 2x = 28; 5 12 days Solve each equation or formula for the specified 36. variable. ANSWER: 45. , for m –7 ANSWER: 37. ANSWER: –3 46. , for a 38. ANSWER: ANSWER: –5

39. 47. , for h

ANSWER: ANSWER: –6

40.

ANSWER: 48. , for y 8 ANSWER:

41.

ANSWER: 49. , for a –3 ANSWER:

42.

ANSWER: 50. , for z 4 ANSWER: 43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: 51. GEOMETRY The formula for the volume of a s = length of a side; 5s = 100; 20 in. cylinder with radius r and height h is times the radius times the height. 44. MEDICINE For Nina’s illness her doctor gives her a. Write this as an algebraic expression. a prescription for 28 pills. The doctor says that she should take 4 pills the first day and then 2 pills each b. Solve the expression in part a for h. day until her prescription runs out. For how many ANSWER: days does she take 2 pills? a. ANSWER: b. x = the number of days she takes 2 pills; 4 + 2x = 28;

12 days 52. AWARDS BANQUET A banquet room can seat a Solve each equation or formula for the specified maximum of 69 people. The coach, principal, and variable. vice principal have invited the award-winning girls’ tennis team to the banquet. If the tennis team 45. , for m consists of 22 girls, how many guests can each ANSWER: student bring? ANSWER: n = number of guests that each student can bring; 22n + 25 = 69; 2 guests

46. , for a Solve each equation. Check your solution. 53. ANSWER: ANSWER: –2

47. , for h 54. ANSWER: ANSWER: 3

48. , for y 55. ANSWER: ANSWER: –4

56. 49. , for a ANSWER: ANSWER: 3

57.

50. , for z ANSWER: ANSWER:

52. AWARDS BANQUET A banquet room can seat a month? maximum of 69 people. The coach, principal, and vice principal have invited the award-winning girls’ tennis team to the banquet. If the tennis team consists of 22 girls, how many guests can each student bring?

ANSWER: ANSWER: n = number of guests that each student can bring; 22n + 25 = 69; 2 guests x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month Solve each equation. Check your solution. 53. 60. BRIDGES The Sunshine Skyway Bridge spans Tampa Bay, Florida. Suppose one crew began ANSWER: building south from St. Petersburg, and another crew –2 began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg approximately 5 years after construction began.

54. a. Suppose the St. Petersburg crew built an average of 176 feet per month. Together the two crews built ANSWER: 21,120 feet of bridge. Determine the average number of feet built per month by the Bradenton crew. 3 b. About how many miles of bridge did each crew 55. build? c. Is this answer reasonable? Explain. ANSWER: ANSWER: –4 a. 176 ft 56. b. 2 mi c. Yes; it seems reasonable that two crews working ANSWER: 4 miles apart would be able to complete the same 3 amount of miles in the same amount of time.

61. MULTIPLE REPRESENTATIONS The absolute 57. value of a number describes the distance of the number from zero. ANSWER: a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the number line and their distance from zero. 58. c. GRAPHICAL Make a graph of each integer x and its distance from zero y using the data points in the table. ANSWER: d. VERBAL Make a conjecture about the integer and its distance from zero. Explain the reason for any changes in sign.

59. FINANCIAL LITERACY Benjamin spent $10,734 ANSWER: on his living expenses last year. Most of these a. expenses are listed at the right. Benjamin’s only other expense last year was rent. If he paid rent 12 times last year, how much is Benjamin’s rent each b. month?

ANSWER: x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month

60. BRIDGES The Sunshine Skyway Bridge spans Tampa Bay, Florida. Suppose one crew began c. building south from St. Petersburg, and another crew began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg approximately 5 years after construction began. a. Suppose the St. Petersburg crew built an average of 176 feet per month. Together the two crews built 21,120 feet of bridge. Determine the average number of feet built per month by the Bradenton crew. b. About how many miles of bridge did each crew build? d. For positive integers, the distance from zero is the c. Is this answer reasonable? Explain. same as the integer. For negative integers, the distance is the integer with the opposite sign because ANSWER: distance is always positive. a. 176 ft b. 2 mi 62. ERROR ANALYSIS Steven and Jade are solving c. Yes; it seems reasonable that two crews working 4 miles apart would be able to complete the same for b2. Is either of them correct? amount of miles in the same amount of time. Explain your reasoning. 61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the number from zero. a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. ANSWER: b. TABULAR Create a table of the integers on the Sample answer: Jade; in the last step, when Steven number line and their distance from zero. subtracted b from each side, he mistakenly put the – c. GRAPHICAL Make a graph of each integer x 1 and its distance from zero y using the data points in b1 in the numerator instead of after the entire the table. fraction. d. VERBAL Make a conjecture about the integer and its distance from zero. Explain the reason for any 63. CHALLENGE Solve changes in sign. for y1 ANSWER: a. ANSWER:

65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no solution and another example that has infinitely many d. For positive integers, the distance from zero is the solutions. same as the integer. For negative integers, the 1-3 Solvingdistance Equationsis the integer with the opposite sign because ANSWER: distance is always positive. Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2

b1 in the numerator instead of after the entire fraction.

63. CHALLENGE Solve

for y1 ANSWER:

A. C.

64. REASONING Use what you have learned in this B. D. lesson to explain why the following number trick works. ANSWER: • Take any number. D • Multiply it by ten. • Subtract 30 from the result. • Divide the new result by 5. 68. SAT/ACT What is subtracted from its • Add 6 to the result. reciprocal? • Your new number is twice your original. F ANSWER: Translating this number trick into an expression G

yields: H

ANSWER: 65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no G solution and another example that has infinitely many solutions. 69. GEOMETRY Which of the following describes the transformation of to ? ANSWER: Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2 eSolutions66. WRITINGManual - Powered IN MATHby Cognero Compare and contrast the Page 6 Substitution Property of Equality and the Transitive Property of Equality. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property A. a reflection across the y-axis and a translation is done with two values, that is, one being substituted down 2 units for another, the Transitive Property deals with three B. a reflection across the x-axis and a translation values, determining that since two values are equal to down 2 units a third value, then they must be equal. C. a rotation to the right and a translation down 67. The graph shows the solution of which inequality? 2 units D. a rotation to the right and a translation right 2 units ANSWER: A

70. SHORT RESPONSE A local theater sold 1200 tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What was the percent decrease of tickets sold? A. C. ANSWER:

B. D. 71. Simplify . ANSWER: D ANSWER: –3x + 6y + 6z 68. SAT/ACT What is subtracted from its 72. BAKING Tamera is making two types of bread. reciprocal? The first type of bread needs cups of flour, and F

the second needs cups of flour. Tamera wants to G make 2 loaves of the first recipe and 3 loaves of the

H second recipe. How many cups of flour does she need?

J ANSWER:

ANSWER: 73. LANDMARKS Suppose the Space Needle in G Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If 69. GEOMETRY Which of the following describes the the tourist is feet tall, how tall is the Space transformation of to ? Needle?

A. a reflection across the y-axis and a translation down 2 units B. a reflection across the x-axis and a translation ANSWER: down 2 units 605 ft C. a rotation to the right and a translation down 2 units 74. Evaluate , if a = 5, b = 7, and c = 2. D. a rotation to the right and a translation right 2 units ANSWER: ANSWER: 1 A Identify the additive inverse for each number or expression. 70. SHORT RESPONSE A local theater sold 1200

tickets during the opening weekend of a movie. On 75. the following weekend, 840 tickets were sold. What

was the percent decrease of tickets sold? ANSWER: ANSWER:

71. Simplify . 76. 3.5 ANSWER: ANSWER: –3x + 6y + 6z 72. BAKING Tamera is making two types of bread. 77. The first type of bread needs cups of flour, and ANSWER: 2x the second needs cups of flour. Tamera wants to

make 2 loaves of the first recipe and 3 loaves of the 78. second recipe. How many cups of flour does she ANSWER: need?

ANSWER:

79.

ANSWER: 73. LANDMARKS Suppose the Space Needle in Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If

the tourist is feet tall, how tall is the Space 80. Needle? ANSWER: 1.25

81. ANSWER:

82. ANSWER: ANSWER: 605 ft

74. Evaluate , if a = 5, b = 7, and c = 2.

ANSWER: 1 Identify the additive inverse for each number or expression.

75.

ANSWER:

76. 3.5 ANSWER:

77. ANSWER: 2x

78. ANSWER:

79.

ANSWER:

80. ANSWER: 1.25

81. ANSWER:

82. ANSWER:

Write an algebraic expression to represent each verbal expression. 1. the product of 12 and the sum of a number and negative 3 ANSWER:

2. the difference between the product of 4 and a number and the square of the number ANSWER: 2 4x – x

Write a verbal sentence to represent each equation. 3. ANSWER: The sum of five times a number and 7 equals 18.

4. ANSWER: The difference between the square of a number and 9 is 27.

5. ANSWER: The difference between five times a number and the cube of that number is 12.

ANSWER: Eight more than the quotient of a number and four is –16.

Name the property illustrated by each statement. 7.

ANSWER: Reflexive Property

8. If and , then . Write an algebraic expression to represent each verbal expression. ANSWER: 1. the product of 12 and the sum of a number and Transitive Property negative 3 Solve each equation. Check your solution. ANSWER: 9. ANSWER: 53 2. the difference between the product of 4 and a number and the square of the number 10. ANSWER: ANSWER: 2 4x – x –6 Write a verbal sentence to represent each 11. equation. 3. ANSWER: ANSWER: –8 The sum of five times a number and 7 equals 18. 12.

4. ANSWER: –7 ANSWER: The difference between the square of a number and 13. 9 is 27. ANSWER: 5. –6 ANSWER: 14. The difference between five times a number and the cube of that number is 12. ANSWER: –4 6. 15. ANSWER: Eight more than the quotient of a number and four is ANSWER: –16. 3

Name the property illustrated by each 16. statement. 7. ANSWER: 8 ANSWER: Reflexive Property 17.

8. If and , then . ANSWER: 4 ANSWER: Transitive Property 18. Solve each equation. Check your solution. ANSWER: 9. –5 ANSWER: 53 Solve each equation or formula for the specified variable. 10. 19. ,for q ANSWER: ANSWER: –6

11. 20. , for n ANSWER: –8 ANSWER:

12. ANSWER: –7 21. MULTIPLE CHOICE If , what is the

13. value of ? ANSWER: A –10 –6 B –3 C 1 14. D 5 ANSWER: ANSWER: –4 B

15. Write an algebraic expression to represent each verbal expression. ANSWER: 22. the difference between the product of four and a number and 6 3 ANSWER: 16. ANSWER: 23. the product of the square of a number and 8 8 ANSWER: 17. 8x2

ANSWER: 24. fifteen less than the cube of a number 4 ANSWER: 3 18. x – 15

ANSWER: 25. five more than the quotient of a number and 4 –5 ANSWER:

Solve each equation or formula for the specified variable. 19. ,for q Write a verbal sentence to represent each ANSWER: equation.

26. ANSWER: Four less than 8 times a number is 16. 20. , for n

ANSWER: 27.

ANSWER: The quotient of the sum of 3 and a number and 4 is 5. 21. MULTIPLE CHOICE If , what is the 28. value of ? ANSWER: A –10 Three less than four times the square of a number is B –3 13. C 1 D 5 29. BASEBALL During a recent season, Miguel Cabrera and Mike Jacobs of the Florida Marlins hit a ANSWER: combined total of 46 home runs. Cabrera hit 6 more B home runs than Jacobs. How many home runs did each player hit? Define a variable, write an equation, Write an algebraic expression to represent and solve the problem. each verbal expression. 22. the difference between the product of four and a ANSWER: number and 6 n = number of home runs Jacobs hit; n + 6 = number of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 ANSWER: home runs, Cabrera: 26 home runs.

Name the property illustrated by each statement. 23. the product of the square of a number and 8 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 ANSWER: ANSWER: 2 8x 30. Subtr. (=) 24. fifteen less than the cube of a number 31. If y = –3, then 7y = 7(–3) ANSWER: ANSWER: 3 x – 15 Subst. 25. five more than the quotient of a number and 4 32. If g = 3h and 3h = 16, then g = 16 ANSWER: ANSWER: Transitive Property

33. If –y = 13, then –(–y) = –13 Write a verbal sentence to represent each equation. ANSWER: 26. Mult. (=) ANSWER: 34. MONEY Aiko and Kendra arrive at the state fair Four less than 8 times a number is 16. with $32.50. What is the total number of rides they can go on if they each pay the entrance fee?

27.

ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

28. ANSWER: Three less than four times the square of a number is ANSWER: 13. n = number of rides; 2(7.50) + n(2.50) = 32.50; 7

29. BASEBALL During a recent season, Miguel Solve each equation. Check your solution. Cabrera and Mike Jacobs of the Florida Marlins hit a 35. combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did ANSWER: each player hit? Define a variable, write an equation, 5 and solve the problem. ANSWER: 36. n = number of home runs Jacobs hit; n + 6 = number ANSWER: of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 –7 home runs, Cabrera: 26 home runs.

Name the property illustrated by each 37. statement. ANSWER: 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 –3 ANSWER: 30. Subtr. (=) 38. ANSWER: 31. If y = –3, then 7y = 7(–3) –5 ANSWER: 39. Subst. ANSWER: 32. If g = 3h and 3h = 16, then g = 16 –6 ANSWER: Transitive Property 40.

33. If –y = 13, then –(–y) = –13 ANSWER: 8 ANSWER: Mult. (=) 41. 34. MONEY Aiko and Kendra arrive at the state fair with $32.50. What is the total number of rides they ANSWER: can go on if they each pay the entrance fee? –3

42.

ANSWER: 4

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: ANSWER: s = length of a side; 5s = 100; 20 in. n = number of rides; 2(7.50) + n(2.50) = 32.50; 7 44. MEDICINE For Nina’s illness her doctor gives her Solve each equation. Check your solution. a prescription for 28 pills. The doctor says that she 35. should take 4 pills the first day and then 2 pills each day until her prescription runs out. For how many ANSWER: days does she take 2 pills? 5 ANSWER: x = the number of days she takes 2 pills; 4 + 2x = 28; 36. 12 days ANSWER: Solve each equation or formula for the specified –7 variable. 37. 45. , for m ANSWER: ANSWER: –3

38.

ANSWER: 46. , for a –5 ANSWER: 39.

ANSWER: –6 47. , for h

40. ANSWER:

ANSWER: 8 48. , for y 41. ANSWER: ANSWER: –3 49. , for a 42. ANSWER: ANSWER: 4

43. GEOMETRY The perimeter of a regular pentagon 50. , for z is 100 inches. Find the length of each side. ANSWER: ANSWER: s = length of a side; 5s = 100; 20 in.

MEDICINE 44. For Nina’s illness her doctor gives her 51. GEOMETRY The formula for the volume of a a prescription for 28 pills. The doctor says that she cylinder with radius r and height h is times the should take 4 pills the first day and then 2 pills each radius times the height. day until her prescription runs out. For how many days does she take 2 pills? a. Write this as an algebraic expression. b. Solve the expression in part a for h. ANSWER: ANSWER: x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days a. b. Solve each equation or formula for the specified variable. 52. AWARDS BANQUET A banquet room can seat a

45. , for m maximum of 69 people. The coach, principal, and ANSWER: vice principal have invited the award-winning girls’ tennis team to the banquet. If the tennis team consists of 22 girls, how many guests can each student bring? ANSWER: 46. , for a n = number of guests that each student can bring; ANSWER: 22n + 25 = 69; 2 guests Solve each equation. Check your solution. 53.

47. , for h ANSWER: –2 ANSWER:

54.

48. , for y ANSWER: 3 ANSWER: 55.

ANSWER: 49. , for a –4

ANSWER: 56. ANSWER: 3 50. , for z ANSWER: 57.

ANSWER:

51. GEOMETRY The formula for the volume of a cylinder with radius r and height h is times the radius times the height. 58. a. Write this as an algebraic expression. b. Solve the expression in part a for h. ANSWER: ANSWER: a. b. 59. FINANCIAL LITERACY Benjamin spent $10,734 on his living expenses last year. Most of these 52. AWARDS BANQUET A banquet room can seat a expenses are listed at the right. Benjamin’s only maximum of 69 people. The coach, principal, and other expense last year was rent. If he paid rent 12 vice principal have invited the award-winning girls’ times last year, how much is Benjamin’s rent each tennis team to the banquet. If the tennis team month? consists of 22 girls, how many guests can each student bring? ANSWER: n = number of guests that each student can bring; 22n + 25 = 69; 2 guests Solve each equation. Check your solution. ANSWER: 53. x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month ANSWER: –2 60. BRIDGES The Sunshine Skyway Bridge spans Tampa Bay, Florida. Suppose one crew began building south from St. Petersburg, and another crew 54. began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg ANSWER: approximately 5 years after construction began. 3 a. Suppose the St. Petersburg crew built an average of 176 feet per month. Together the two crews built 55. 21,120 feet of bridge. Determine the average number of feet built per month by the Bradenton crew. ANSWER: b. About how many miles of bridge did each crew –4 build? c. Is this answer reasonable? Explain. 56. ANSWER: ANSWER: a. 176 ft 3 b. 2 mi c. Yes; it seems reasonable that two crews working 57. 4 miles apart would be able to complete the same amount of miles in the same amount of time.

ANSWER: 61. MULTIPLE REPRESENTATIONS The absolute value of a number describes the distance of the number from zero. a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. 58. b. TABULAR Create a table of the integers on the number line and their distance from zero. ANSWER: c. GRAPHICAL Make a graph of each integer x and its distance from zero y using the data points in the table. d. VERBAL Make a conjecture about the integer 59. FINANCIAL LITERACY Benjamin spent $10,734 and its distance from zero. Explain the reason for any on his living expenses last year. Most of these changes in sign. expenses are listed at the right. Benjamin’s only other expense last year was rent. If he paid rent 12 ANSWER: times last year, how much is Benjamin’s rent each a. month?

ANSWER: x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month

60. BRIDGES The Sunshine Skyway Bridge spans Tampa Bay, Florida. Suppose one crew began building south from St. Petersburg, and another crew began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg c. approximately 5 years after construction began. a. Suppose the St. Petersburg crew built an average of 176 feet per month. Together the two crews built 21,120 feet of bridge. Determine the average number of feet built per month by the Bradenton crew. b. About how many miles of bridge did each crew build? c. Is this answer reasonable? Explain. ANSWER: d. For positive integers, the distance from zero is the a. 176 ft same as the integer. For negative integers, the b. 2 mi distance is the integer with the opposite sign because c. Yes; it seems reasonable that two crews working distance is always positive. 4 miles apart would be able to complete the same amount of miles in the same amount of time. 62. ERROR ANALYSIS Steven and Jade are solving

61. MULTIPLE REPRESENTATIONS The absolute for b2. Is either of them correct? value of a number describes the distance of the Explain your reasoning. number from zero. a. GEOMETRIC Draw a number line. Label the integers from –5 to 5. b. TABULAR Create a table of the integers on the number line and their distance from zero. c. GRAPHICAL Make a graph of each integer x ANSWER: and its distance from zero y using the data points in Sample answer: Jade; in the last step, when Steven the table. subtracted b from each side, he mistakenly put the – d. VERBAL Make a conjecture about the integer 1 and its distance from zero. Explain the reason for any b1 in the numerator instead of after the entire changes in sign. fraction. ANSWER: 63. CHALLENGE Solve a. for y1

b. ANSWER:

c. ANSWER: Translating this number trick into an expression yields:

d. For positive integers, the distance from zero is the 65. OPEN ENDED Provide one example of an equation same as the integer. For negative integers, the involving the Distributive Property that has no distance is the integer with the opposite sign because solution and another example that has infinitely many distance is always positive. solutions. 62. ERROR ANALYSIS Steven and Jade are solving ANSWER: Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2 for b2. Is either of them correct? Explain your reasoning. 66. WRITING IN MATH Compare and contrast the Substitution Property of Equality and the Transitive Property of Equality. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property ANSWER: is done with two values, that is, one being substituted Sample answer: Jade; in the last step, when Steven for another, the Transitive Property deals with three subtracted b1 from each side, he mistakenly put the – values, determining that since two values are equal to a third value, then they must be equal. b1 in the numerator instead of after the entire fraction. 67. The graph shows the solution of which inequality? 63. CHALLENGE Solve

for y1 ANSWER:

64. REASONING Use what you have learned in this

lesson to explain why the following number trick A. C. works.

• Take any number. B. D. • Multiply it by ten. • Subtract 30 from the result. ANSWER: • Divide the new result by 5. D • Add 6 to the result. • Your new number is twice your original. 68. SAT/ACT What is subtracted from its ANSWER: reciprocal? Translating this number trick into an expression yields: F

OPEN ENDED 65. Provide one example of an equation K involving the Distributive Property that has no solution and another example that has infinitely many solutions. ANSWER: G ANSWER: Sample answer: 3(x – 4) = 3x + 5; 2(3x – 1) = 6x – 2 69. GEOMETRY Which of the following describes the transformation of to ? 66. WRITING IN MATH Compare and contrast the Substitution Property of Equality and the Transitive Property of Equality. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property is done with two values, that is, one being substituted for another, the Transitive Property deals with three values, determining that since two values are equal to A. a reflection across the y-axis and a translation a third value, then they must be equal. down 2 units 67. The graph shows the solution of which inequality? B. a reflection across the x-axis and a translation down 2 units C. a rotation to the right and a translation down 2 units D. a rotation to the right and a translation right 2 units ANSWER: A

70. SHORT RESPONSE A local theater sold 1200 A. C. tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What

B. D. was the percent decrease of tickets sold? ANSWER: ANSWER: D 71. Simplify . 68. SAT/ACT What is subtracted from its ANSWER: reciprocal? –3x + 6y + 6z F 72. BAKING Tamera is making two types of bread.

G The first type of bread needs cups of flour, and

H the second needs cups of flour. Tamera wants to

J make 2 loaves of the first recipe and 3 loaves of the second recipe. How many cups of flour does she need? K ANSWER: 1-3 SolvingANSWER: Equations G

69. GEOMETRY Which of the following describes the 73. LANDMARKS Suppose the Space Needle in transformation of to ? Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If the tourist is feet tall, how tall is the Space Needle?

A. a reflection across the y-axis and a translation down 2 units B. a reflection across the x-axis and a translation down 2 units C. a rotation to the right and a translation down 2 units ANSWER: D. a rotation to the right and a translation right 2 605 ft units ANSWER: 74. Evaluate , if a = 5, b = 7, and c = 2. A ANSWER: 70. SHORT RESPONSE A local theater sold 1200 1 tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What Identify the additive inverse for each number or was the percent decrease of tickets sold? expression.

ANSWER: 75.

ANSWER: 71. Simplify . ANSWER: –3x + 6y + 6z 76. 3.5 72. BAKING Tamera is making two types of bread. ANSWER: The first type of bread needs cups of flour, and

the second needs cups of flour. Tamera wants to 77. make 2 loaves of the first recipe and 3 loaves of the ANSWER: second recipe. How many cups of flour does she 2x need? 78. ANSWER: ANSWER:

73. LANDMARKS Suppose the Space Needle in 79. Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If ANSWER: eSolutionsthe touristManual is- Powered feet tallby Cognero, how tall is the Space Page 7 Needle? 80. ANSWER: 1.25

81. ANSWER:

ANSWER: 82. 605 ft ANSWER:

74. Evaluate , if a = 5, b = 7, and c = 2.

ANSWER: 1 Identify the additive inverse for each number or expression.

75.

ANSWER:

76. 3.5 ANSWER:

77. ANSWER: 2x

78. ANSWER:

79.

ANSWER:

80. ANSWER: 1.25

81. ANSWER:

82. ANSWER:

Write an algebraic expression to represent each verbal expression. 1. the product of 12 and the sum of a number and negative 3 ANSWER:

2. the difference between the product of 4 and a number and the square of the number ANSWER: 2 4x – x

Write a verbal sentence to represent each equation. 3. ANSWER: The sum of five times a number and 7 equals 18.

4. ANSWER: The difference between the square of a number and 9 is 27.

5. ANSWER: The difference between five times a number and the cube of that number is 12.

ANSWER: Eight more than the quotient of a number and four is –16.

Name the property illustrated by each statement. 7.

ANSWER: Reflexive Property

8. If and , then . ANSWER: Transitive Property

Solve each equation. Check your solution. 9. ANSWER: 53

10. ANSWER: –6

11. ANSWER: –8

12. ANSWER: –7

13. ANSWER: –6

14. ANSWER: –4

15.

ANSWER: 3

16.

ANSWER: 8

17.

ANSWER: 4

18.

ANSWER: –5

Solve each equation or formula for the specified variable. 19. ,for q ANSWER:

20. , for n ANSWER:

21. MULTIPLE CHOICE If , what is the

value of ? A –10 B –3 C 1 D 5 ANSWER: B

Write an algebraic expression to represent each verbal expression. 22. the difference between the product of four and a number and 6 ANSWER:

23. the product of the square of a number and 8 ANSWER: 8x2

24. fifteen less than the cube of a number ANSWER: 3 x – 15

25. five more than the quotient of a number and 4 ANSWER:

Write a verbal sentence to represent each equation. 26. ANSWER: Four less than 8 times a number is 16.

27.

ANSWER: The quotient of the sum of 3 and a number and 4 is 5.

28. ANSWER: Three less than four times the square of a number is 13.

29. BASEBALL During a recent season, Miguel Cabrera and Mike Jacobs of the Florida Marlins hit a combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did each player hit? Define a variable, write an equation, and solve the problem. ANSWER: n = number of home runs Jacobs hit; n + 6 = number of home runs Cabrera hit; 2n + 6 = 46; Jacobs: 20 home runs, Cabrera: 26 home runs.

Name the property illustrated by each statement. 30. If x + 9 = 2, then x + 9 – 9 = 2 – 9 ANSWER: 30. Subtr. (=)

31. If y = –3, then 7y = 7(–3) ANSWER: Subst. 32. If g = 3h and 3h = 16, then g = 16 ANSWER: Transitive Property

33. If –y = 13, then –(–y) = –13 ANSWER: Mult. (=)

34. MONEY Aiko and Kendra arrive at the state fair with $32.50. What is the total number of rides they can go on if they each pay the entrance fee?

ANSWER: n = number of rides; 2(7.50) + n(2.50) = 32.50; 7

Solve each equation. Check your solution. 35. ANSWER: 5

36. ANSWER: –7

37. ANSWER: –3

38. ANSWER: –5

39.

ANSWER: –6

40.

ANSWER: 8

41.

ANSWER: –3

42.

ANSWER: 4

43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side. ANSWER: s = length of a side; 5s = 100; 20 in.

44. MEDICINE For Nina’s illness her doctor gives her a prescription for 28 pills. The doctor says that she should take 4 pills the first day and then 2 pills each day until her prescription runs out. For how many days does she take 2 pills? ANSWER: x = the number of days she takes 2 pills; 4 + 2x = 28; 12 days

Solve each equation or formula for the specified variable. 45. , for m ANSWER:

46. , for a

ANSWER:

47. , for h ANSWER:

48. , for y

ANSWER:

49. , for a ANSWER:

50. , for z ANSWER:

51. GEOMETRY The formula for the volume of a cylinder with radius r and height h is times the radius times the height. a. Write this as an algebraic expression. b. Solve the expression in part a for h. ANSWER: a. b.

52. AWARDS BANQUET A banquet room can seat a maximum of 69 people. The coach, principal, and vice principal have invited the award-winning girls’ tennis team to the banquet. If the tennis team consists of 22 girls, how many guests can each student bring? ANSWER: n = number of guests that each student can bring; 22n + 25 = 69; 2 guests

Solve each equation. Check your solution. 53. ANSWER: –2

54.

ANSWER: 3

55.

ANSWER: –4

56. ANSWER: 3

57.

ANSWER:

58.

ANSWER:

59. FINANCIAL LITERACY Benjamin spent $10,734 on his living expenses last year. Most of these expenses are listed at the right. Benjamin’s only other expense last year was rent. If he paid rent 12 times last year, how much is Benjamin’s rent each month?

ANSWER: x = the cost of rent each month; 622 + 428 + 240 + 144 + 12x = 10,734; $775 per month

60. BRIDGES The Sunshine Skyway Bridge spans Tampa Bay, Florida. Suppose one crew began building south from St. Petersburg, and another crew began building north from Bradenton. The two crews met 10,560 feet south of St. Petersburg approximately 5 years after construction began. a. Suppose the St. Petersburg crew built an average of 176 feet per month. Together the two crews built 21,120 feet of bridge. Determine the average number of feet built per month by the Bradenton crew. b. About how many miles of bridge did each crew build? c. Is this answer reasonable? Explain. ANSWER: a. 176 ft b. 2 mi c. Yes; it seems reasonable that two crews working 4 miles apart would be able to complete the same amount of miles in the same amount of time.

d. For positive integers, the distance from zero is the same as the integer. For negative integers, the distance is the integer with the opposite sign because distance is always positive.

62. ERROR ANALYSIS Steven and Jade are solving

for b2. Is either of them correct? Explain your reasoning.

ANSWER: Sample answer: Jade; in the last step, when Steven subtracted b1 from each side, he mistakenly put the –

b1 in the numerator instead of after the entire fraction.

63. CHALLENGE Solve

for y1 ANSWER:

66. WRITING IN MATH Compare and contrast the Substitution Property of Equality and the Transitive Property of Equality. ANSWER: Sample answer: The Transitive Property utilizes the Substitution Property. While the Substitution Property is done with two values, that is, one being substituted for another, the Transitive Property deals with three values, determining that since two values are equal to a third value, then they must be equal.

67. The graph shows the solution of which inequality?

A. C.

B. D.

ANSWER: D

68. SAT/ACT What is subtracted from its reciprocal? F

ANSWER: G

69. GEOMETRY Which of the following describes the transformation of to ?

70. SHORT RESPONSE A local theater sold 1200 tickets during the opening weekend of a movie. On the following weekend, 840 tickets were sold. What was the percent decrease of tickets sold? ANSWER:

71. Simplify . ANSWER: –3x + 6y + 6z

72. BAKING Tamera is making two types of bread. The first type of bread needs cups of flour, and

the second needs cups of flour. Tamera wants to make 2 loaves of the first recipe and 3 loaves of the second recipe. How many cups of flour does she need? ANSWER:

73. LANDMARKS Suppose the Space Needle in Seattle, Washington, casts a 220-foot shadow at the same time a nearby tourist casts a 2-foot shadow. If the tourist is feet tall, how tall is the Space Needle?

ANSWER: 605 ft

74. Evaluate , if a = 5, b = 7, and c = 2.

ANSWER: 1 Identify the additive inverse for each number or expression.

75.

ANSWER:

76. 3.5 ANSWER:

77. ANSWER: 2x

78.

1-3 SolvingANSWER: Equations

79.

ANSWER:

80. ANSWER: 1.25

81. ANSWER:

82. ANSWER: