1. COMPOUND INEQUALITIES

2. Compound Inequality

3. Compound Inequality
Two inequalities joined by the word “and” or the word “or”

4. Compound Inequality
Two inequalities joined by the word “and” or the word “or” Example: −5<𝑥<0

5. Compound Inequality
Two inequalities joined by the word “and” or the word “or” Example: −5<𝑥<0 This is read: “- 5 is less than x, and x is less than 0”

6. Compound Inequality
Example: 4≤𝑦≤12

7. Compound Inequality
Example: 4≤𝑦≤12 This is read: “4 is less than or equal to x, and x is less than or equal to 12”

8. Graphing

9. Graphing
4≤𝑥<10

10. Graphing
4≤𝑥<10
To graph, graph the individual inequalities

11. Graphing
4≤𝑥<10
To graph, graph the individual inequalities 4 10

12. Graphing
4≤𝑥<10
To graph, graph the individual inequalities 4 10

13. Graphing
4≤𝑥<10
To graph, graph the individual inequalities 4 10

14. Graphing
4≤𝑥<10
To graph, graph the individual inequalities 4 10

15. Graphing
4≤𝑥<10
To graph, graph the individual inequalities 4 10

16. Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10
If the graphed areas will cross, draw one line

17. Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10
If the graphed areas will cross, draw one line 4 10

18. Writing
All real numbers greater than -2, but less than 9

19. Writing
All real numbers greater than -2, but less than 9 Have r stand for the real numbers

20. Writing
All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9

21. Writing
All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9
Graph

22. Writing
All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9
Graph -2 9

23. Writing
All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9
Graph -2 9

24. Writing
All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9
Graph -2 9

25. Writing
All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9
Graph -2 9

26. Writing
Temperatures from 32oF to 40oF, inclusive.

27. Writing
Temperatures from 32oF to 40oF, inclusive. Inclusive means “to include”

28. Writing
Temperatures from 32oF to 40oF, inclusive. Inclusive means “to include” 32≤𝑡≤40

29. Solving

30. Solving
−6≤3𝑥<15

31. Solving
−6≤3𝑥<15
Break the compound inequality into the two parts.

32. Solving −6≤3𝑥<15 Break the compound inequality into the two parts.
−6≤3𝑥 𝑥<15

33. Solving −6≤3𝑥<15 Break the compound inequality into the two parts.
−6≤3𝑥 𝑥<15
Solve each inequality

34. Solving −6≤3𝑥<15 Break the compound inequality into the two parts.
−6≤3𝑥 𝑥<15
Solve each inequality
−2≤𝑥 𝑥<5

35. Solving −6≤3𝑥<15 Break the compound inequality into the two parts.
−6≤3𝑥 𝑥<15
Solve each inequality
−2≤𝑥 𝑥<5
Combine back into one compound inequality

36. Solving −6≤3𝑥<15 Break the compound inequality into the two parts.
−6≤3𝑥 𝑥<15
Solve each inequality
−2≤𝑥 𝑥<5
Combine back into one compound inequality
−2≤𝑥<5

37. Solving −6≤3𝑥<15 Break the compound inequality into the two parts.
−6≤3𝑥 𝑥<15
Solve each inequality
−2≤𝑥 𝑥<5
Combine back into one compound inequality
−2≤𝑥<5
Choose a value that fits the inequality statement.

38. Solving −6≤3𝑥<15 Break the compound inequality into the two parts.
−6≤3𝑥 𝑥<15
Solve each inequality
−2≤𝑥 𝑥<5
Combine back into one compound inequality
−2≤𝑥<5
Choose a value that fits the inequality statement.
The value must work for both sides of the compound inequality.

39. Solving

40. Solving
−3≤2𝑥−1<7

41. Solving
−3≤2𝑥−1<7
−3≤2𝑥−1

42. Solving
−3≤2𝑥−1<7
−3≤2𝑥−1
−2≤2𝑥

43. Solving
−3≤2𝑥−1<7
−3≤2𝑥−1
−2≤2𝑥
−1≤𝑥

44. Solving
−3≤2𝑥−1<7
−3≤2𝑥−1
2𝑥−1<7
−2≤2𝑥
−1≤𝑥

45. Solving
−3≤2𝑥−1<7
−3≤2𝑥−1
2𝑥−1<7
−2≤2𝑥
2𝑥<8
−1≤𝑥

46. Solving
−3≤2𝑥−1<7
−3≤2𝑥−1
2𝑥−1<7
−2≤2𝑥
2𝑥<8
−1≤𝑥
𝑥<4

47. Solving −3≤2𝑥−1<7 −3≤2𝑥−1 2𝑥−1<7 −2≤2𝑥 2𝑥<8 −1≤𝑥 𝑥<4
−1≤𝑥<4

48. Solving
7<−3𝑛+1≤13

49. Solving
7<−3𝑛+1≤13
7<−3𝑛+1

50. Solving
7<−3𝑛+1≤13
7<−3𝑛+1
−3𝑛+1≤13

51. Solving
7<−3𝑛+1≤13
7<−3𝑛+1
−3𝑛+1≤13
6<−3𝑛

52. Solving
7<−3𝑛+1≤13
7<−3𝑛+1
−3𝑛+1≤13
6<−3𝑛
−2>𝑛

53. Solving
7<−3𝑛+1≤13
7<−3𝑛+1
−3𝑛+1≤13
6<−3𝑛
−3𝑛≤12
−2>𝑛

54. Solving
7<−3𝑛+1≤13
7<−3𝑛+1
−3𝑛+1≤13
6<−3𝑛
−3𝑛≤12
𝑛≥−4
−2>𝑛

55. Solving 7<−3𝑛+1≤13 7<−3𝑛+1 −3𝑛+1≤13 6<−3𝑛 −3𝑛≤12 𝑛≥−4 −2>𝑛
−2>𝑛≥−4

56. Applications
Your test scores in science so far are 83 and What possible grades can you have on your next test to have an average between 85 and 90, inclusive?

57. Your test scores in science so far are 83 and 87
Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive? 1. What are you trying to find?

58. Your test scores in science so far are 83 and 87
Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive? 1. What are you trying to find? 2. How do you find an average?

59. Your test scores in science so far are 83 and 87
Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive? 1. What are you trying to find? 2. How do you find an average? 3. Write your inequality statement.

60. Your test scores in science so far are 83 and 87
Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive? 1. What are you trying to find? 2. How do you find an average? 3. Write your inequality statement. 85≤ 𝑡 ≤90

61. 85≤ 𝑡 ≤90

62. 85≤ 𝑡 ≤90
85≤ 𝑡 ≤90

63. 85≤ 𝑡 ≤90
85≤ 𝑡 ≤90
85≤ 𝑡+170 3
𝑡 ≤90

64. 85≤ 𝑡 ≤90
85≤ 𝑡 ≤90
85≤ 𝑡+170 3
𝑡 ≤90
255≤𝑡+170

65. 85≤ 𝑡 ≤90
85≤ 𝑡 ≤90
85≤ 𝑡+170 3
𝑡 ≤90
255≤𝑡+170
85≤𝑡

66. 85≤ 𝑡 ≤90
85≤ 𝑡 ≤90
85≤ 𝑡+170 3
𝑡 ≤90
255≤𝑡+170
𝑡+170≤270
85≤𝑡

67. 85≤ 𝑡 ≤90
85≤ 𝑡 ≤90
85≤ 𝑡+170 3
𝑡 ≤90
255≤𝑡+170
𝑡+170≤270
85≤𝑡
𝑡≤100

68. 85≤ 𝑡 ≤90
85≤ 𝑡 ≤90
85≤ 𝑡+170 3
𝑡 ≤90
255≤𝑡+170
𝑡+170≤270
85≤𝑡
𝑡≤100
85≤𝑡≤100

69. 85≤ 𝑡 ≤90
85≤ 𝑡 ≤90
85≤ 𝑡+170 3
𝑡 ≤90
255≤𝑡+170
𝑡+170≤270
85≤𝑡
𝑡≤100
85≤𝑡≤100
So your next test score must be between 85 and 100, inclusive.

70. Assignment
3.5A: 1 – 19,