1. 1.4 – Solving Absolute Value Equations

2. Absolute Value

3. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only

4. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only

5. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs)

6. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5|

7. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5

8. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| =

9. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1

10. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3

11. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=

12. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4

13. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 +

14. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5

15. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3)

16. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7|

17. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4

18. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 +

19. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15

20. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15 – 7|

21. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15 – 7| =1.4

22. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15 – 7| =1.4 +

23. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15 – 7| =1.4 + |-22|

24. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15 – 7| =1.4 + |-22| =1.4

25. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15 – 7| =1.4 + |-22| =1.4 +

26. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15 – 7| =1.4 + |-22| =1.4 + 22

27. 1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| = 5 Example 1 Evaluate 1.4+|5y – 7| if y=-3 1.4+|5y – 7|=1.4 + |5(-3) – 7| =1.4 + |-15 – 7| =1.4 + |-22| =1.4 + 22 = 23.4

28. Example 2

29. Example 2 Solve |x – 18| = 5.

30. |x – 18| = 5

31. Example 2 Solve |x – 18| = 5. |x – 18| = 5

32. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5

33. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5

34. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5

35. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5

36. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5

37. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18

38. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 x = 23

39. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23

40. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13

41. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3

42. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0.

43. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0

44. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9

45. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9 |5x – 6| = -9

46. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9 |5x – 6| = -9 Note:

47. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

48. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

49. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

50. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

51. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

52. Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3 Solve |5x – 6| + 9 = 0. |5x – 6| + 9 = 0 -9 |5x – 6| = -9 Note: Absolute value cannot equal a negative number! x = Ø

53. Example 4

54. Example 4 Solve |x + 6| = 3x – 2.

55. |x + 6| = 3x – 2

56. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2

57. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2

58. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2

59. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2)

60. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2)

61. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6

62. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 =

63. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x

64. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x –

65. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2)

66. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2

67. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6

68. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x

69. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2

70. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x

71. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -2x + 6 = -2

72. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6

73. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x

74. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8

75. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2

76. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2 x = 4

77. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2 x = 4

78. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x - 6 -6 -2x = -8 -2 -2 x = 4

79. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 - 6 -6 -2x = -8 -2 -2 x = 4

80. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 -2x = -8 -2 -2 x = 4

81. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -8 -2 -2 x = 4

82. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 x = 4

83. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4

84. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1

85. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1

86. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1

87. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1

88. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1

89. Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2) x + 6 = 3x – 2 x + 6 = -3x + 2 -3x -3x +3x +3x -2x + 6 = -24x + 6 = 2 - 6 -6 - 6 -6 -2x = -84x = -4 -2 -2 4 4 x = 4 OR x = -1