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Algebra 1B Section 5-4
 

Algebra 1B Section 5-4

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Compound Inequalities

Compound Inequalities

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    Algebra 1B Section 5-4 Algebra 1B Section 5-4 Presentation Transcript

    • Section 5-4 Compound Inequalities Monday, October 14, 13
    • Essential Question ✤ How do you solve compound inequalities? Monday, October 14, 13
    • Vocabulary 1. Compound Inequality: 2. Intersection: 3. Union: Monday, October 14, 13
    • Vocabulary 1. Compound Inequality: Two inequalities that are utilized at the same time 2. Intersection: 3. Union: Monday, October 14, 13
    • Vocabulary 1. Compound Inequality: Two inequalities that are utilized at the same time 2. Intersection: A compound inequality the connects the two inequalities using and; Only true if BOTH inequalities are true 3. Union: Monday, October 14, 13
    • Vocabulary 1. Compound Inequality: Two inequalities that are utilized at the same time 2. Intersection: A compound inequality the connects the two inequalities using and; Only true if BOTH inequalities are true 3. Union: A compound inequality the connects the two inequalities using or; True if EITHER inequality is true Monday, October 14, 13
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 Monday, October 14, 13 x + 2 ≤ 11
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 Monday, October 14, 13 and x + 2 ≤ 11
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 Monday, October 14, 13 and x + 2 ≤ 11
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 5<x Monday, October 14, 13 and x + 2 ≤ 11
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 5<x Monday, October 14, 13 and x + 2 ≤ 11 −2 −2
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 5<x Monday, October 14, 13 and x + 2 ≤ 11 −2 −2 x≤9
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 5<x 0 Monday, October 14, 13 and 5 x + 2 ≤ 11 −2 −2 x≤9 10
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 5<x 0 Monday, October 14, 13 and 5 x + 2 ≤ 11 −2 −2 x≤9 10
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 5<x 0 Monday, October 14, 13 and 5 x + 2 ≤ 11 −2 −2 x≤9 10
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 5<x 0 Monday, October 14, 13 and 5 x + 2 ≤ 11 −2 −2 x≤9 10
    • Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 −2 −2 5<x 0 Monday, October 14, 13 and {x|5 < x ≤ 9} 5 x + 2 ≤ 11 −2 −2 x≤9 10
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 Monday, October 14, 13 12 − 9k ≥ 30
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 Monday, October 14, 13 or 12 − 9k ≥ 30
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 Monday, October 14, 13 or 12 − 9k ≥ 30
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 Monday, October 14, 13 or 12 − 9k ≥ 30
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 Monday, October 14, 13 or 12 − 9k ≥ 30
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 Monday, October 14, 13 or 12 − 9k ≥ 30
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 Monday, October 14, 13 or 12 − 9k ≥ 30 −12 −12
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 Monday, October 14, 13 or 12 − 9k ≥ 30 −12 −12 −9k ≥ 18
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 Monday, October 14, 13 or 12 − 9k ≥ 30 −12 −12 −9k ≥ 18 −9 −9
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 Monday, October 14, 13 or 12 − 9k ≥ 30 −12 −12 −9k ≥ 18 −9 −9 k ≤ −2
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 -2 Monday, October 14, 13 0 12 − 9k ≥ 30 −12 −12 −9k ≥ 18 −9 −9 k ≤ −2 or 2 4 6 8
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 -2 Monday, October 14, 13 0 12 − 9k ≥ 30 −12 −12 −9k ≥ 18 −9 −9 k ≤ −2 or 2 4 6 8
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 -2 Monday, October 14, 13 0 12 − 9k ≥ 30 −12 −12 −9k ≥ 18 −9 −9 k ≤ −2 or 2 4 6 8
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 -2 Monday, October 14, 13 0 12 − 9k ≥ 30 −12 −12 −9k ≥ 18 −9 −9 k ≤ −2 or 2 4 6 8
    • Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 +7 +7 4k ≤ 32 4 4 k≤8 -2 Monday, October 14, 13 0 12 − 9k ≥ 30 −12 −12 −9k ≥ 18 −9 −9 {k|k ≤ 8} k ≤ −2 or 2 4 6 8
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 Monday, October 14, 13 3y + 4 < −5
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 Monday, October 14, 13 or 3y + 4 < −5
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 Monday, October 14, 13 or 3y + 4 < −5
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 Monday, October 14, 13 or 3y + 4 < −5
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 Monday, October 14, 13 or 3y + 4 < −5
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 Monday, October 14, 13 or 3y + 4 < −5
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 Monday, October 14, 13 or 3y + 4 < −5 −4 −4
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 Monday, October 14, 13 or 3y + 4 < −5 −4 −4 3y < −9
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 Monday, October 14, 13 or 3y + 4 < −5 −4 −4 3y < −9 3 3
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 Monday, October 14, 13 or 3y + 4 < −5 −4 −4 3y < −9 3 3 y < −3
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 -6 Monday, October 14, 13 3y + 4 < −5 −4 −4 3y < −9 3 3 y < −3 or -4 0 2 4 6
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 -6 Monday, October 14, 13 3y + 4 < −5 −4 −4 3y < −9 3 3 y < −3 or -4 0 2 4 6
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 -6 Monday, October 14, 13 3y + 4 < −5 −4 −4 3y < −9 3 3 y < −3 or -4 0 2 4 6
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 -6 Monday, October 14, 13 3y + 4 < −5 −4 −4 3y < −9 3 3 y < −3 or -4 0 2 4 6
    • Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 3y + 4 < −5 −4 −4 3y < −9 3 3 {y|y < −3} y < −3 −y + 5 ≥ 9 −5 −5 −y ≥ 4 −1 −1 y ≤ −4 -6 Monday, October 14, 13 or -4 0 2 4 6
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 d − 3 < 6d + 12 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 d − 3 < 6d + 12 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −3 < 5d + 12 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −3 < 5d + 12 −12 −12 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −3 < 5d + 12 −12 −12 −15 < 5d Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −3 < 5d + 12 −12 −12 −15 < 5d 5 5 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −3 < 5d + 12 −12 −12 −15 < 5d 5 5 −3 < d Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −3 < 5d + 12 −12 −12 −15 < 5d 5 5 −3 < d d > −3 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 −12 −12 −15 < 5d 5 5 −3 < d d > −3 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −15 < 5d 5 5 −3 < d d > −3 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 5 5 −3 < d d > −3 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 4d < 20 5 5 −3 < d d > −3 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 4d < 20 4 4 5 5 −3 < d d > −3 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 4d < 20 4 4 5 5 d<5 −3 < d d > −3 Monday, October 14, 13
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 4d < 20 4 4 5 5 d<5 −3 < d d > −3 -6 Monday, October 14, 13 -4 0 2 4 6
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 4d < 20 4 4 5 5 d<5 −3 < d d > −3 -6 Monday, October 14, 13 -4 0 2 4 6
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 4d < 20 4 4 5 5 d<5 −3 < d d > −3 -6 Monday, October 14, 13 -4 0 2 4 6
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 4d < 20 4 4 5 5 d<5 −3 < d d > −3 -6 Monday, October 14, 13 -4 0 2 4 6
    • Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 6d + 12 < 2d + 32 and d − 3 < 6d + 12 −d −d −2d −2d −3 < 5d + 12 4d + 12 < 32 −12 −12 −12 −12 −15 < 5d 4d < 20 {d|−3 < d < 5} 4 4 5 5 d<5 −3 < d d > −3 -6 Monday, October 14, 13 -4 0 2 4 6
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. Monday, October 14, 13
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Monday, October 14, 13
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room Monday, October 14, 13
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room Monday, October 14, 13 Cabin
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room c ≤ 89 Monday, October 14, 13 Cabin
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room c ≤ 89 Monday, October 14, 13 Cabin c ≥ 109
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room Cabin c ≤ 89 c ≥ 109 86 Monday, October 14, 13 90 94 98 102 106 110
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room Cabin c ≤ 89 c ≥ 109 86 Monday, October 14, 13 90 94 98 102 106 110
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room Cabin c ≤ 89 c ≥ 109 86 Monday, October 14, 13 90 94 98 102 106 110
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room Cabin c ≤ 89 c ≥ 109 86 Monday, October 14, 13 90 94 98 102 106 110
    • Example 2 A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. c = cost per night Room Cabin c ≤ 89 c ≥ 109 {c|c ≤ 89 or c ≥ 109} 86 Monday, October 14, 13 90 94 98 102 106 110
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. Monday, October 14, 13
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. n = number Monday, October 14, 13
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. n = number n − 8 ≤ 14 Monday, October 14, 13
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. n = number n − 8 ≤ 14 Monday, October 14, 13 n−8≥ 5
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. n = number n − 8 ≤ 14 +8 +8 Monday, October 14, 13 n−8≥ 5
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. n = number n − 8 ≤ 14 +8 +8 n ≤ 22 Monday, October 14, 13 n−8≥ 5
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. n = number n − 8 ≤ 14 +8 +8 n ≤ 22 Monday, October 14, 13 n−8≥ 5 +8 +8
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. n = number n − 8 ≤ 14 +8 +8 n ≤ 22 Monday, October 14, 13 n−8≥ 5 +8 +8 n ≥ 13
    • Example 3 Write a compound inequality and solve. a. Eight less than a number is no more than fourteen and no less than five. n = number n − 8 ≤ 14 +8 +8 n ≤ 22 n−8≥ 5 +8 +8 n ≥ 13 {n|13 ≤ n ≤ 22} Monday, October 14, 13
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. Monday, October 14, 13
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. n = number Monday, October 14, 13
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. n = number −5n > 35 Monday, October 14, 13
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. n = number −5n > 35 Monday, October 14, 13 −5n < 10
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. n = number −5n > 35 −5 −5 Monday, October 14, 13 −5n < 10
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. n = number −5n > 35 −5 −5 n < −7 Monday, October 14, 13 −5n < 10
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. n = number −5n > 35 −5 −5 n < −7 Monday, October 14, 13 −5n < 10 −5 −5
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. n = number −5n > 35 −5 −5 n < −7 Monday, October 14, 13 −5n < 10 −5 −5 n > −2
    • Example 3 Write a compound inequality and solve. b. The product of negative five and a number is greater than thirty five or less than ten. n = number −5n > 35 −5 −5 n < −7 −5n < 10 −5 −5 n > −2 {n|n < −7 or n > −2} Monday, October 14, 13
    • Summarizer Write a compound inequality for which the graph is the empty set and one for which the graph is the set of all real numbers. Monday, October 14, 13
    • Problem Sets Monday, October 14, 13
    • Problem Sets Problem Set 1: p. 306 #1-5 all, 7-15 odd Problem Set 2: p. 306 #16, 17-27 odd, 28, 29, 31, 33-36 all “It is always easier to believe than to deny. Our minds are naturally affirmative." - John Burroughs Monday, October 14, 13