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1.6 – Solving Compound and Absolute Value Inequalities.

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1 1.6 – Solving Compound and Absolute Value Inequalities

2 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 + 7 2x + 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 + 7 2x + 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 + 7 2x + 7 ≤ 17 -7

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 + 7 2x + 7 ≤ 17 -7 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 + 7 2x + 7 ≤ 17 -7 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 + 7 2x + 7 ≤ 17 -7 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 + 7 2x + 7 ≤ 17 -7 6 < 2x 2 2

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 + 7 2x + 7 ≤ 17 -7 6 < 2x 2 2 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 + 7 2x + 7 ≤ 17 -7 6 < 2x 2 2 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 + 7 2x + 7 ≤ 17 -7 6 < 2x 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x < 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x < 10 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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 + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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

37

38 y – 2 > -3 or y + 4 ≤ -3

39 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

40 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 +2 +2 -4 -4

41 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 +2 +2 -4 -4 y > -1 or y ≤ -7

42 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 +2 +2 -4 -4 y > -1 or y ≤ -7

43 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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

44 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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

45 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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

46 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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

47 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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

48 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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

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

52 Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 -4 04

53 Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 (b) Solve |a| > 4. Graph the solution on a number line. -4 04

54 Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 (b) Solve |a| > 4. Graph the solution on a number line. |a| > 4 -4 04

55 Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 (b) Solve |a| > 4. Graph the solution on a number line. |a| > 4 a > 4 or a < -4 -4 04

56 Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 (b) Solve |a| > 4. Graph the solution on a number line. |a| > 4 a > 4 or a < -4 -4 04 04

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

58 |3x – 12| ≥ 6

59 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 solution on a number line. |3x – 12| ≥ 6 3x – 12 ≥ 6 3x – 12 < -6

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

62 Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line. |3x – 12| ≥ 6 3x – 12 ≥ 6 3x – 12 < -6 +12 +12 _ +12 +12 3x ≥ 18 3x < 6

63 Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line. |3x – 12| ≥ 6 3x – 12 ≥ 6 3x – 12 < -6 +12 +12 _ +12 +12 3x ≥ 18 3x < 6 3 3 3 3

64 Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line. |3x – 12| ≥ 6 3x – 12 ≥ 6 3x – 12 < -6 +12 +12 _ +12 +12 3x ≥ 18 3x < 6 3 3 3 3 x ≥ 6 x < 2

65 Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line. |3x – 12| ≥ 6 3x – 12 ≥ 6 3x – 12 < -6 +12 +12 _ +12 +12 3x ≥ 18 3x < 6 3 3 3 3 x ≥ 6 x < 2 0 26


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