5-1 Solving Inequalities by Addition and Subtraction Solve each inequality. Then graph the solution set on a number line. x 3 > 7 The solution set is {x | x > 10}. y The solution set is {y | y 2}. g + 6 < 2 The solution set is {g | g < 4}. p + 4 The solution set is {p | p n eSolutions Manual - Powered by Cognero Page 1 Solve each inequality. Then graph the solution set on a number line. x 3 > 7 The solution set is {x | x > 10}. y The solution set is {y | y 2}. g + 6 < 2 The solution set is {g | g < 4}. p + 4 The solution set is {p | p 5-1 Solving Inequalities by Addition and Subtraction 10 > n 1 The solution set is {n | n < 11}. k + 24 > 5 The solution set is {k | k > 29}. 8r + 6 < 9r The solution set is {r | r > 6}. 8nn 3 The solution set is {n | n 3}. Define a variable, write an inequality, and solve each problem. Check your solution. Twice a number increased by 4 is at least 10 more than the number. Let n = the number. eSolutions Manual - Powered by Cognero Page 2 The solution set is {n | n }. To check substitute three different values into the original inequality: 6, a number less than 6, and a number greater than 6. The inequality is true when n is greater than or equal to 6, so the solution checks. Three more than a number is less than twice the number. Let n = the number. The solution set is {n | n > 3}. To check substitute three different values into the original inequality: 3, a number less than 3, and a number greater than 3. The inequality is true when n is greater than 3, so the solution checks. A thrill ride swings passengers back and forth, a little higher each time up to 137 feet. Suppose the height of the swing after 30 seconds is 45 feet. How much higher will the ride swing? The ride will swing no higher than 92 more feet. Solve each inequality. Then graph the solution set on a number line. m 4 < 3 The solution set is {m | m < 7}. p The solution set is {p | p r The solution set is {r | r t 3 > 8 The solution set is {t | t > 5}. b The solution set is {b | b 13 > 18 + r The solution set is {r | r < 5}. 5 + c The solution set is {c | c 4}. q 30 The solution set is {q | q 11 + m The solution set is {m | m h 26 < 4 The solution set is {h | h < 30}. r 14 The solution set is {r | r 7 > 20 + c The solution set is {c | c < 27}. 2a 4 + a The solution set is {a | a 4}. z z The solution set is {z | z w w The solution set is {w | w 5}. 3yy The solution set is {y | y 6}. 6xx The solution set is {x | x 9 + 2a < 3a The solution set is {a | a > 9}. Define a variable, write an inequality, and solve each problem. Check your solution. Twice a number is more than the sum of that number and 9. Let n = the number. The solution set is {n | n >9}. To check substitute three different values into the original inequality: 9, a number less than 9, and a number greater than 9. The inequality is true when n is greater than 9, so the solution checks. The sum of twice a number and 5 is at most 3 less than the number. Let n = the number. The solution set is {n | n8}. To check substitute three different values into the original inequality: 8, a number less than 8, and a number greater than 8. The inequality is true when n is equal to or less than 8, so the solution checks. The sum of three times a number and 4 is at least twice the number plus 8. Let n = the number. The solution set is {n | n To check substitute three different values into the original inequality: 12, a number less than 12, and a number greater than 12. The inequality is true when n is greater than or equal to 12, so the solution checks. Six times a number decreased by 8 is less than five times the number plus 21. Let n = the number. The solution set is {n | n < 29}. To check substitute three different values into the original inequality: 29, a number less than 29, and a number greater than 29. The inequality is true when n is less than 29, so the solution checks. Define a variable, write an inequality, and solve each problem. Then interpret your solution. Keisha is babysitting at $8 per hour to earn money for a car. So far she has saved $1300. The car that Keisha wants to buy costs at least $5440. How much money does Keisha still need to earn to buy the car? Let b = the amount of money that Keisha still needs. The solution set is {b | b A recent survey found that more than 21 million people between the ages of 12 and 17 use the Internet. Of those, about 16 million said they use the Internet at school. How many teens that are online do not use the Internet at school? Let n = the number, in millions, of online teens that do not use the Internet at school. The solution set is {n | n > 5}. So, at least 5 million teens use the Internet somewhere other than school. A DJ added 20 more songs to his digital media player, making the total more than 61. How many songs were originally on the player? Let n = the original number of songs on the player. The solution set is {n | n > 41}. So, there were originally more than 41 songs on the digital media player. Let t = the water temperature in the morning. The solution set is {t | t A players goal was to score at least 150 points this season. So far, she has scored 123 points. If there is one game left, how many points must she score to reach her goal? Let p = the number of points the basket ball player must score to reach her goal. The solution set is {p | p Samantha received a $75 gift card for a local day spa for her birthday. She plans to get a hair cut and a manicure. How much money will be left on her gift card after her visit? Service Cost ($) Hair Cut at least 32 Manicure at least 26 Let m = the amount of money left on the gift card. The solution set is {m | ms gift card. Kono knows that he can only volunteer up to 25 hours per week. If he has volunteered for the times recorded below, how much more time can Kono volunteer this week? Center Time (h) Shelter 3 h 15 min Kitchen 2 h 20 min Let t = the amount of time, in hours, left in the week for Kono to volunteer. The solution set is . So, Kono can volunteer at most 19 hours and 25 minutes more this week. Solve each inequality. Check your solution, and then graph it on a number line. c + ( The solution set is {c | c To check substitute three different values into the original inequality: 3.7, a number less than 3.7, and a number greater than 3.7. The inequality is true when c is equal to or greater than 3.7, so the solution checks. 9.1g + 4.5 < 10.1g The solution set is {g | g > 4.5}. To check substitute three different values into the original inequality: 4.5, a number less than 4.5, and a number greater than 4.5. The inequality is true when g is greater than 4.5, so the solution checks. The solution set is . To check substitute three values into the original inequality: , a number less than , and a number greater than . The inequality is true when k is greater than , so the solution checks. The solution set is . To check substitute three different values into the original inequality: , a number less than , and a number greater than . The inequality is true when p is equal to or less than , so the solution checks. In this problem, you will explore multiplication and division in inequalities. Suppose a balance has 12 pounds on the left side and 18 pounds on the right side. Draw a picture to represent this situation. Write an inequality to represent the situation. Create a table showing the result of doubling, tripling, or quadrupling the weight on each side of the balance. Create a second table showing the result of reducing the weight on each side of the balance by a factor of , , or . Include a column in each table for the inequality representing each situation. Describe the effect multiplying or dividing each side of an inequality by the same positive value has on the inequality. a. 12 lb < 18 lb c. 12 18 x2 24 36 x3 36 54 x4 48 72 12 18 6 9 x 4 6 x 3 x If a true inequality is multiplied by a positive number, the resulting inequality is also true. If a true inequality is divided by a positive number, the resulting inequality is also true. If m m ? So, ? = 17. m + ? So, ? = 10. m ? So, ? = 12. m ? So, ? = 3. m ? So, ? = 2. m + ? So, ? = 26. Compare and contrast the graphs of a < 4 and a In both graphs, the line is darkened to the left of 4.