The document discusses solving absolute value equations. It explains that absolute value is the distance a number is from 0, and provides examples. It then states that when solving absolute value equations, two separate equations must be created to account for the number inside the absolute value being positive or negative. Steps are provided for solving sample absolute value equations.

1. Solving Absolute Value
Equations

2. Absolute Value
Absolute Value is the distance a number is from 0.

3. Absolute Value
Absolute Value is the distance a number is from 0.
|3| = 3 and |-3| = 3

4. Absolute Value
Absolute Value is the distance a number is from 0.
|3| = 3 and |-3| = 3
When solving an absolute value equation, you need
to account for the number inside the absolute value
could be positive OR negative.

5. Absolute Value
Absolute Value is the distance a number is from 0.
|3| = 3 and |-3| = 3
When solving an absolute value equation, you need
to account for the number inside the absolute value
could be positive OR negative.
So 2 equation must be created to solve absolute
value equations.

6. Solve for x:
x−5 =8

7. Solve for x:
x−5 =8
Split into 2
equations.

8. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.

9. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
Solve each
equation.

10. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
+5 +5
Solve each
equation.

11. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
+5 +5
Solve each
x = 13 equation.

12. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
+5 +5 +5 +5
Solve each
x = 13 equation.

13. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
+5 +5 +5 +5
Solve each
x = 13 equation. x = −3

14. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
+5 +5 +5 +5
Solve each
x = 13 equation. x = −3
Check both
solutions.

15. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
+5 +5 +5 +5
Solve each
x = 13 equation. x = −3
?
Check both
13 − 5 = 8
solutions.
?
8 =8
8=8

16. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
+5 +5 +5 +5
Solve each
x = 13 equation. x = −3
?
?
Check both −3 − 5 = 8
13 − 5 = 8
solutions. ?
?
−8 = 8
8 =8
8=8
8=8

17. Solve for x:
x−5 =8
x−5=8 Split into 2 x − 5 = −8
equations.
+5 +5 +5 +5
Solve each
x = 13 equation. x = −3
?
?
Check both −3 − 5 = 8
13 − 5 = 8
solutions. ?
?
Write answer. −8 = 8
8 =8
8=8
8=8 {−3,13}

18. Solve for x:
2x + 1 = 7

19. Solve for x:
2x + 1 = 7
Split into 2
equations.

20. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
equations.

21. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
equations.
Solve each
equation.

22. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations.
Solve each
equation.

23. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations.
Solve each
2x = 6 equation.

24. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations.
Solve each
2x = 6 equation.
2 2

25. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations.
Solve each
2x = 6 equation.
2 2
x=3

26. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations. −1 −1
Solve each
2x = 6 equation.
2 2
x=3

27. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations. −1 −1
Solve each
2x = 6 equation. 2x = −8
2 2
x=3

28. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations. −1 −1
Solve each
2x = 6 equation. 2x = −8
2 2 2 2
x=3

29. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations. −1 −1
Solve each
2x = 6 equation. 2x = −8
2 2 2 2
x=3 x = −4

30. Solve for x:
2x + 1 = 7
2x + 1 = 7 Split into 2 2x + 1 = −7
−1 −1 equations. −1 −1
Solve each
2x = 6 equation. 2x = −8
2 2 Check both 2 2
solutions on
x=3 next page. x = −4

31. Solve for x continued...
2x + 1 = 7
x=3 Check both
x = −4
solutions.
Write answer.

32. Solve for x continued...
2x + 1 = 7
x=3 Check both
x = −4
? solutions.
2 ( 3) + 1 = 7 Write answer.
?
7 =7
7=7

33. Solve for x continued...
2x + 1 = 7
x=3 Check both
x = −4
? solutions. ?
2 ( 3) + 1 = 7 2 ( −4 ) + 1 = 7
Write answer.
? ?
7 =7 −7 = 7
7=7 7=7

34. Solve for x continued...
2x + 1 = 7
x=3 Check both
x = −4
? solutions. ?
2 ( 3) + 1 = 7 2 ( −4 ) + 1 = 7
Write answer.
? ?
7 =7 −7 = 7
7=7
{−4, 3} 7=7

35. Solve for x:
x − 5 = 2x

36. Solve for x:
x − 5 = 2x
Split into 2
equations.

37. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
equations.

38. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
equations.
Solve each
equation.

39. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations.
Solve each
equation.

40. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations.
Solve each
−5 = x equation.

41. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations. +2x +2x
Solve each
−5 = x equation.

42. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations. +2x +2x
Solve each 3x − 5 = 0
−5 = x equation.

43. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations. +2x +2x
Solve each 3x − 5 = 0
−5 = x equation. +5 +5

44. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations. +2x +2x
Solve each 3x − 5 = 0
−5 = x equation. +5 +5
3x = 5

45. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations. +2x +2x
Solve each 3x − 5 = 0
−5 = x equation. +5 +5
3x = 5
3 3

46. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations. +2x +2x
Solve each 3x − 5 = 0
−5 = x equation. +5 +5
3x = 5
3 3
5
x=
3

47. Solve for x:
x − 5 = 2x
x − 5 = 2x Split into 2 x − 5 = −2x
−x −x equations. +2x +2x
Solve each 3x − 5 = 0
−5 = x equation. +5 +5
Check both
3x = 5
solutions on
next page. 3 3
5
x=
3

48. Solve for x continued...
x − 5 = 2x 5
x=
−5 = x Check both
3
solutions.
Only 1
solution
works. So the
answer is

49. Solve for x continued...
x − 5 = 2x 5
x=
−5 = x Check both
3
?
solutions.
−5 − 5 = 2 ( −5 )
? Only 1
−10 = − 10 solution
10 ≠ −10 works. So the
answer is

50. Solve for x continued...
x − 5 = 2x 5
x=
−5 = x Check both
3
?
solutions. 5 ?
 5
−5 − 5 = 2 ( −5 ) − 5 = 2 
Only 1 3  3
?
−10 = − 10 solution −10 ? 10
=
10 ≠ −10 works. So the 3 3
answer is 10 10
=
3 3

51. Solve for x continued...
x − 5 = 2x 5
x=
−5 = x Check both
3
?
solutions. 5 ?
 5
−5 − 5 = 2 ( −5 ) − 5 = 2 
Only 1 3  3
?
−10 = − 10 solution −10 ? 10
=
10 ≠ −10 works. So the 3 3
answer is 10 10
=
5  3 3
 
3

52. Solve for x:
3x + 7 = x

53. Solve for x:
3x + 7 = x
Split into 2
equations.

54. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
equations.

55. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
equations.
Solve each
equation.

56. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations.
Solve each
equation.

57. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations.
2x + 7 = 0 Solve each
equation.

58. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations.
2x + 7 = 0 Solve each
equation.
−7 −7

59. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations.
2x + 7 = 0 Solve each
equation.
−7 −7
2x = −7

60. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations.
2x + 7 = 0 Solve each
equation.
−7 −7
2x = −7
2 2

61. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations.
2x + 7 = 0 Solve each
equation.
−7 −7
2x = −7
2 2
−7
x=
2

62. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations. +x +x
2x + 7 = 0 Solve each
equation.
−7 −7
2x = −7
2 2
−7
x=
2

63. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations. +x +x
2x + 7 = 0 Solve each 4x + 7 = 0
equation.
−7 −7
2x = −7
2 2
−7
x=
2

64. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations. +x +x
2x + 7 = 0 Solve each 4x + 7 = 0
equation. −7 −7
−7 −7
2x = −7
2 2
−7
x=
2

65. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations. +x +x
2x + 7 = 0 Solve each 4x + 7 = 0
equation. −7 −7
−7 −7
2x = −7 4x = −7
2 2
−7
x=
2

66. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations. +x +x
2x + 7 = 0 Solve each 4x + 7 = 0
equation. −7 −7
−7 −7
2x = −7 4x = −7
2 2 4 4
−7
x=
2

67. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations. +x +x
2x + 7 = 0 Solve each 4x + 7 = 0
equation. −7 −7
−7 −7
2x = −7 4x = −7
2 2 4 4
−7 −7
x= x=
2 4

68. Solve for x:
3x + 7 = x
3x + 7 = x Split into 2 3x + 7 = −x
−x −x equations. +x +x
2x + 7 = 0 Solve each 4x + 7 = 0
equation. −7 −7
−7 −7
Check both 4x = −7
2x = −7 solutions on
2 2 next page. 4 4
−7 −7
x= x=
2 4

69. Solve for x continued...
−7 3x + 7 = x x=
−7
x=
2 Check both 4
solutions.
Neither
solution
works so the
answer is

70. Solve for x continued...
−7 3x + 7 = x x=
−7
x=
2 Check both 4
 −7  ? −7 solutions.
3  + 7 =
 2 2 Neither
solution
−7 ? −7
= works so the
2 2 answer is
7 −7
≠
2 2

71. Solve for x continued...
−7 3x + 7 = x x=
−7
x=
2 Check both 4
 −7  ? −7 solutions.
3  + 7 =  −7  ? −7
 2 Neither 3  + 7 =
2  4 4
solution
−7 ? −7 7 ? −7
= works so the =
2 2 answer is 4 4
7 −7 7 −7
≠ ≠
2 2 4 4

72. Solve for x continued...
−7 3x + 7 = x x=
−7
x=
2 Check both 4
 −7  ? −7 solutions.
3  + 7 =  −7  ? −7
 2 Neither 3  + 7 =
2  4 4
solution
−7 ? −7 7 ? −7
= works so the =
2 2 answer is 4 4
7 −7 7 −7
≠ ≠
2 2 no solution 4 4