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Algebra 1B Section 5-4

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Compound Inequalities

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Algebra 1B Section 5-4

1. 1. Section 5-4 Compound Inequalities Monday, October 14, 13
2. 2. Essential Question ✤ How do you solve compound inequalities? Monday, October 14, 13
3. 3. Vocabulary 1. Compound Inequality: 2. Intersection: 3. Union: Monday, October 14, 13
4. 4. Vocabulary 1. Compound Inequality: Two inequalities that are utilized at the same time 2. Intersection: 3. Union: Monday, October 14, 13
5. 5. 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
6. 6. 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
7. 7. Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 Monday, October 14, 13
8. 8. Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 Monday, October 14, 13
9. 9. Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 Monday, October 14, 13 x + 2 ≤ 11
10. 10. Example 1 Solve and graph the solution set. a. 7 < x + 2 ≤ 11 7< x+2 Monday, October 14, 13 and x + 2 ≤ 11
11. 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
12. 12. 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
13. 13. 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
14. 14. 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
15. 15. 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
16. 16. 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
17. 17. 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
18. 18. 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
19. 19. 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
20. 20. Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 Monday, October 14, 13
21. 21. Example 1 Solve and graph the solution set. b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30 4k − 7 ≤ 25 Monday, October 14, 13
22. 22. 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
23. 23. 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
24. 24. 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
25. 25. 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
26. 26. 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
27. 27. 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
28. 28. 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
29. 29. 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
30. 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 −9k ≥ 18 −9 −9
31. 31. 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
32. 32. 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
33. 33. 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
34. 34. 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
35. 35. 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
36. 36. 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
37. 37. Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 Monday, October 14, 13
38. 38. Example 1 Solve and graph the solution set. c. − y + 5 ≥ 9 or 3y + 4 < −5 −y + 5 ≥ 9 Monday, October 14, 13
39. 39. 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
40. 40. 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
41. 41. 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
42. 42. 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
43. 43. 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
44. 44. 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
45. 45. 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
46. 46. 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
47. 47. 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
48. 48. 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
49. 49. 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
50. 50. 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
51. 51. 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
52. 52. 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
53. 53. 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
54. 54. Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 Monday, October 14, 13
55. 55. Example 1 Solve and graph the solution set. d. d − 3 < 6d + 12 < 2d + 32 d − 3 < 6d + 12 Monday, October 14, 13
56. 56. 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
57. 57. 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
58. 58. 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
59. 59. 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
60. 60. 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
61. 61. 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
62. 62. 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
63. 63. 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
64. 64. 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
65. 65. 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
66. 66. 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
67. 67. 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
68. 68. 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
69. 69. 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
70. 70. 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
71. 71. 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
72. 72. 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
73. 73. 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
74. 74. 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
75. 75. 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
76. 76. 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
77. 77. 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
78. 78. 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
79. 79. 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
80. 80. 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
81. 81. 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
82. 82. 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
83. 83. 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
84. 84. 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
85. 85. 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
86. 86. 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
87. 87. 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
88. 88. 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
89. 89. 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
90. 90. 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
91. 91. 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
92. 92. 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
93. 93. 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
94. 94. 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
95. 95. 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
96. 96. 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
97. 97. 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
98. 98. 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
99. 99. 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
100. 100. 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
101. 101. 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
102. 102. 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
103. 103. 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
104. 104. 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
105. 105. 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
106. 106. Problem Sets Monday, October 14, 13
107. 107. 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