Download x ≥ 6

5-4 Solving Compound Inequalities
16. SPEED The posted speed limit on an interstate highway is shown. Write an inequality that represents the sign.
Graph the inequality.
ANSWER: Sample answer: Let r = rate of speed, then 40 ≤ r ≤ 70.
17. NUMBER THEORY Find all sets of two consecutive positive odd integers with a sum that is at least 8 and less
than 24.
ANSWER: Sample answer: Let x = the smaller of two consecutive odd numbers, then 8 ≤ 2x + 2 ≤ 24; 3 ≤ x ≤ 11; 3, 5; 5, 7; 7, 9; 9, 11; 11, 13
Write a compound inequality for each graph.
18. ANSWER: −1 ≤ x ≤ 4
19. ANSWER: −3 < x ≤ 2
20. ANSWER: x < 0 or x ≥ 3
21. ANSWER: x < −4 or x > −3
22. ANSWER: x ≤ 3 or x ≥ 6
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ANSWER: x ≤ -3 or x > 0
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22. ANSWER: 5-4 Solving
Compound Inequalities
x ≤ 3 or x ≥ 6
23. ANSWER: x ≤ -3 or x > 0
Solve each compound inequality. Then graph the solution set.
24. 3b + 2 < 5b − 6 ≤ 2b + 9
ANSWER: {b | 4 < b ≤ 5}
25. −2a + 3 ≥ 6a − 1 > 3a − 10
ANSWER: 26. 10m − 7 < 17m or −6m > 36
ANSWER: {m | m < −6 or m > −1}
27. 5n − 1 < −16 or −3n − 1 < 8
ANSWER: {n | n < −3 or n > −3}
28. COUPON Juanita has a coupon for 10% off any digital camera at a local electronics store. She is looking at digital
cameras that range in price from $100 to $250.
a. How much are the cameras after the coupon is used?
b. If the tax amount is 6.5%, how much should Juanita expect to spend?
ANSWER: a. from $90 to $225 inclusive
b. from $95.85 to $239.63 inclusive
Define a variable, write an inequality, and solve each problem. Then check your solution.
29. Eight less than a number is no more than 14 and no less than 5.
ANSWER: Sample answers given. Let n = the number.
5 ≤ n − 8 ≤ 14; {n|13 ≤ n ≤ 22}
30. The sum of 3 times a number and 4 is between −8 and 10.
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ANSWER: Sample answers given. Let n = the number.
−8 < 3n + 4 < 10; {n | −4 < n < 2}
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29. Eight less than a number is no more than 14 and no less than 5.
ANSWER: Sample answers given. Let n = the number.
5-4 Solving
5 ≤ n − 8Compound
≤ 14; {n|13 Inequalities
≤ n ≤ 22}
30. The sum of 3 times a number and 4 is between −8 and 10.
ANSWER: Sample answers given. Let n = the number.
−8 < 3n + 4 < 10; {n | −4 < n < 2}
31. The product of −5 and a number is greater than 35 or less than 10.
ANSWER: Sample answers given. Let n = the number.
−5n > 35 or −5n < 10; {n | n < −7 or n > −2}
32. One half a number is greater than 0 and less than or equal to 1.
ANSWER: Sample answers given. Let n = the number.
0<
n ≤ 1; {n | 0 < n ≤ 2}
36. GEOMETRY The Triangle Inequality Theorem states that the sum of the measures of any two sides of a
triangle is greater than the measure of the third side.
a. Write and solve three inequalities to express the relationships among the measures of the sides of the triangle
shown.
b. What are four possible lengths for the third side of the triangle?
c. Write a compound inequality for the possible values of x.
ANSWER: a. x + 9 > 4, x > −5; x + 4 > 9, x > 5; 4 + 9 > x, x < 13
b. Sample answer: 6, 9, 10, 11
c. 5 < x < 13
40. CHALLENGE Solve each inequality for x. Assume a is constant and a > 0.
a.
b.
or
ANSWER: a. b.
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