Download Solve each compound inequality. Then graph the solution set. 11

5-4 Solving Compound Inequalities
Solve each compound inequality. Then graph the solution set.
11. −3 ≤ 7c + 4 < 18
ANSWER: {c | −1 ≤ c < 2}
13. 22 ≥ 4m − 2 or 5 − 3m ≤ −13
ANSWER: {m|m is a real number.}
15. −y + 5 ≥ 9 or 3y + 4 < −5
ANSWER: {y | y < –3}
17. NUMBER THEORY Find all sets of two consecutive positive odd integers with a sum that is at least 8 and less
than or equal to 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.
19. ANSWER: −3 < x ≤ 2
21. ANSWER: x < −4 or x > −3
23. ANSWER: x ≤ -3 or x > 0
Solve each compound inequality. Then graph the solution set.
25. −2a + 3 ≥ 6a − 1 > 3a − 10
ANSWER: eSolutions Manual - Powered by Cognero
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23. ANSWER: 5-4 Solving
Compound Inequalities
x ≤ -3 or x > 0
Solve each compound inequality. Then graph the solution set.
25. −2a + 3 ≥ 6a − 1 > 3a − 10
ANSWER: 27. 5n − 1 < −16 or −3n − 1 < 8
ANSWER: {n | n < −3 or n > −3}
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}
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}
33. SNAKES Most snakes live where the temperature ranges from 75°F to 90°F inclusive. Write an inequality to represent temperatures where snakes will not thrive.
ANSWER: t < 75 or t > 90
35. TURTLES Atlantic sea turtle eggs that incubate below 23°C or above 33°C rarely hatch. Write the temperature requirements in two ways: as a pair of simple inequalities, and as a compound inequality.
ANSWER: 23 ≤ t ≤ 33 23 ≤ t and t ≤ 33
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.
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b. What are four possible lengths for the third side of the triangle?
c. Write a compound inequality for the possible values of x.
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requirements in two ways: as a pair of simple inequalities, and as a compound inequality.
ANSWER: 23 ≤ t ≤ Compound
33 5-4 Solving
Inequalities
23 ≤ t and t ≤ 33
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
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