Absolute Value Equations

Name: ______Date: ______

Directions: Solve each equation algebraically.

1. 14 = |x| + 3

2. ¾ = |x| - 5

3. |x + 8| = 12

4. -7 = |x - 3| - 10

5. 6.5 = |x + 9| - 14

6. - ¾ |x + 7| - 1 = 3

7. |x + 2| = 3

8. |x + 1| + 5 = 8

9. |3x - 2| + 4 = 6

10. 2|x + 1| - 6 = 4

11. -3|x - 4| + 2 = -7

12. ½|3x + 2| = 7

13. |2x - 3| = 9

14. |5x - 2| + 3 = 11

15. ½|x + 3| + 2 = 3

16. 4 + |x - 8| = 5

Algebraic Properties in Solving Equations

Directions: Name the property that each equation illustrates.

1. 83 + 6 = 6 + 832. 1 • 4y = 4y
3. (8 • 7) • 6 = 8 • (7 • 6)4. 3(a + 2b) = 3a + 6b
5. 7 + (8 + 15) = (7 + 8) + 156. 9 + (-9) = 0

7. 7x + 2y = 2y + 7x8. 15x + 15y = 15(x + y)
9. 10 + 0 = 1010. 5(-3) = (-3)5

Directions: Show the operations (the work) andjustify each step by stating the property of equality used.

11. 5x + 16 = 5112.

5x = 35 ______4y + 8 = -20 ______

x = 7 ______4y = -28 ______

y = -7 ______

13. 4 + 6m + 12 = 14m – 814. 2(k + 3) + 18 = 4k – 10

16 + 6m = 14m – 8 ______2k + 6 + 18 = 4k – 10 ______

16 = 8m – 8 ______2k + 24 = 4k – 10 ______

24 = 8m ______24 = 2k – 10 ______

3 = m ______34 = 2k ______
17 = k ______