1. 1.6 – Solving Compound and Absolute Value Inequalities

2. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

3. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17

4. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17

5. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7

6. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7

7. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x + 7

8. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17

9. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17

10. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17

11. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17 6

12. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 <

13. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x

14. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x

15. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x 3

16. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x
3 <

17. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x
3 < x

18. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x
3 < x

19. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x
3 < x

20. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x <
3 < x

21. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x < 10
3 < x

22. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x

23. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x

24. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x <

25. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x < 5

26. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x < 5

27. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x < 5
3 < x

28. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x ≤ 5
3 < x

29. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x ≤ 5
3 < x < 5

30. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x ≤ 5
3 < x ≤ 5

31. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x ≤ 5
3 < x ≤ 5 3 5

32. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x ≤ 5
3 < x ≤ 5 3 5

33. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x ≤ 5
3 < x ≤ 5 3 5

34. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x ≤ 5
3 < x ≤ 5 3 5

35. 1.6 – Solving Compound and Absolute Value Inequalities
Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.
13 < 2x + 7 ≤ 17
13 < 2x x + 7 ≤ 17
6 < 2x x ≤ 10
3 < x x ≤ 5
3 < x ≤ 5 3 5

36. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

37. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

38. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3

39. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3

40. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3

41. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3
y > or y ≤ -7

42. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3
y > or y ≤ -7

43. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3
y > or y ≤ -7 -7 -1

44. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3
y > or y ≤ -7 -7 -1

45. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3
y > or y ≤ -7 -7 -1

46. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3
y > or y ≤ -7 -7 -1

47. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3
y > or y ≤ -7 -7 -1

48. Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.
y – 2 > -3 or y + 4 ≤ -3
y – 2 > or y + 4 ≤ -3
y > or y ≤ -7 -7 -1

49. Example 3
(a) Solve |a| < 4. Graph the solution on a number line.

50. Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4

51. Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4

52. (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4 -4 4

53. (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
(b) Solve |a| > 4. Graph the solution on a number line. -4 4

54. (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
(b) Solve |a| > 4. Graph the solution on a number line.
|a| > 4 -4 4

55. (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
(b) Solve |a| > 4. Graph the solution on a number line.
|a| > 4
a > or a < -4 -4 4

56. (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4
Example 3
(a) Solve |a| < 4. Graph the solution on a number line.
|a| < 4
a < 4 or a > -4
(b) Solve |a| > 4. Graph the solution on a number line.
|a| > 4
a > or a < -4 -4 4 -4 4

57. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

58. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6

59. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ 6

60. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ x – 12 < -6

61. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ x – 12 < -6 _

62. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ x – 12 < -6 _
3x ≥ x < 6

63. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ x – 12 < -6 _
3x ≥ x < 6

64. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ x – 12 < -6 _
3x ≥ x < 6
x ≥ x < 2

65. Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.
|3x – 12| ≥ 6
3x – 12 ≥ x – 12 < -6 _
3x ≥ x < 6
x ≥ x < 2 2 6