Study Guide and Review - Chapter 5. Solve each inequality. Then graph it on a number line. 11. w 4 > 9 SOLUTION: The solution set is {w w > 13}.
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1 Solve each inequality. Then graph it on a number line. 11. w 4 > 9 The solution set is {w w > 13} h < 1 The solution set is {h h < 5} p 15 The solution set is {p p 2}. 17. FIELD TRIP A bus can hold 44 people. If there are 35 students in Samantha s class, how many more people can ride on the bus? The bus holds a maximum of 44 people. Let s equal how many more students can ride the bus. Write an inequality. The solution set is {s s 9}. So, no more than 9 more students can ride the bus. esolutions Manual - Powered by Cognero Page 1
2 18. Solve each inequality. Graph the solution on a number line. The solution set is {x x > 18} p < 32 The solution set is {p p < 8} m > 100 The solution set is {m m < 50}. esolutions Manual - Powered by Cognero Page 2
3 24. MOVIE RENTAL Jack has no more than $24 to spend on DVDs for a party. Each DVD rents for $4. Find the maximum number of DVDs Jack can rent for his party. The phrase no more than means the same as less than or equal to. Let d be the number of DVDs Jack rents. Write an inequality. The solution set is {d d 6}. So, the maximum number of DVDs Jack can rent is 6. Solve each inequality. Graph the solution on a number line h 7 < 14 The solution set is {h h < 7} x + 8 The solution set is {x x 5}. esolutions Manual - Powered by Cognero Page 3
4 29. Four times a number decreased by 6 is less than 2. Define a variable, write an inequality, and solve for the number. Let x = the number. The solution set is {x x < 1}. 30. TICKET SALES The drama club collected $160 from ticket sales for the spring play. They need to collect at least $400 to pay for new lighting for the stage. If tickets sell for $3 each, how many more tickets need to be sold? The phrase at least means the same as greater than or equal to. Let t be the number of tickets that still need to be sold. Write an inequality. The solution set is {t t 80}. So, at least 80 more tickets need to be sold. Solve each compound inequality. Then graph the solution set. 31. m 3 < 6 and m + 2 > 4 and The solution set is {m 2 < m < 9}. To graph the solution set, graph m < 9 and graph m > 2. Then find the intersection. esolutions Manual - Powered by Cognero Page 4
5 32. 4 < 2t 6 < 8 First, express 4 < 2t 6 < 8 using and. Then solve each inequality. and The solution set is {t 1 < t < 7}. To graph the solution set, graph t > 1 and graph t < 7. Then find the intersection x or 5x 8 > 22 or The solution set is {x x 3 or x > 6}. Notice that the graphs do not intersect. To graph the solution set, graph x 3 and graph x > 6. Then find the union. 34. KITES A large dragon kite can be flown in wind speeds no less than 7 miles per hour and no more than 16 miles per hour. Write an inequality for the wind speeds at which the kite can fly. Let x be the wind speed. The phrase no less than means the same as greater or equal to. The phrase no more than means the same as less than or equal to. The word and indicates that the problem represents an intersection. x 7 and x 16 So, an inequality that represents the wind speeds for which the kite can be flown is 7 x 16. esolutions Manual - Powered by Cognero Page 5
6 Solve each inequality. Then graph the solution set. 35. Case 1 x 4 is positive. and Case 2 x 4 is negative. The solution set is {x 5 < x < 13}. 37. Case 1 2c + 3 is positive. and Case 2 2c + 3 is negative. The solution set is {c 7 c 4}. esolutions Manual - Powered by Cognero Page 6
7 41. Case 1 is positive. or Case 2 is negative. The solution set is {t t < 13 or t > 7}. esolutions Manual - Powered by Cognero Page 7
8 44. Case 1 k 7 is positive. or Case 2 k 7 is negative. The solution set is {k k 3 or k 11}. esolutions Manual - Powered by Cognero Page 8
9 Graph each inequality. 45. y > x 3 y > x 3 Because the inequality involves >, graph the boundary using a dashed line. Choose (0, 0) as a test point. Since 0 is greater than 3, shade the half-plane that contains (0, 0). esolutions Manual - Powered by Cognero Page 9
10 47. 3x y 4 Solve for y in terms of x. Because the inequality involves, graph the boundary using a solid line. Choose (0, 0) as a test point. Since 0 is greater than or equal to -4, shade the half-plane that contains (0, 0). esolutions Manual - Powered by Cognero Page 10
and 5-4 Solving Compound Inequalities Solve each compound inequality. Then graph the solution set. p 8 and p
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and 5-4 Solving Compound Inequalities Solve each compound inequality. Then graph the solution set p 8 and p 14 2 SOLUTION:
Solve each compound inequality. Then graph the solution set. 1. 4 p 8 and p 14 2 and The solution set is {p 12 p 16}. To graph the solution set, graph 12 p and graph p 16. Then find the intersection. {p
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