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**Absolute Value Inequality**

Solve & Graph Absolute Value Inequality

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**Remember … 5 5 = 0 = 16 The distance from zero.**

Simplify the following: 1. |-5| = |5| = 3. |8 + (-8)| = |8| + |-8|= 5 5 |0| = 0 8 + 8 = 16 What does absolute value mean? The distance from zero.

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**Solve & Check: |2m – 4| = 8 ✔ ✔ OR -2 = m m = 6 Solve: |2m – 4|=8**

-4 = 2m +4 +4 2m = 12 . . -2 = m m = 6 Check: |2(-2) – 4| = 8 |2(6) – 4| = 8 |-4 – 4| = 8 |12 – 4| = 8 |-8| = 8 |8| = 8 ✔ ✔ 8 = 8 8 = 8

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**Solve & Check: |3n + 2| - 5 = 4n ✗ ✔ ✗ OR n = -3 n = -1**

|3n + 2| = 4n + 5 -(4n + 5) = 3n + 2 OR 3n + 2 = 4n + 5 -4n - 5 = 3n + 2 -4n n - 2 -n = 3 -3n n + 5 -7n = 7 ✗ n = -3 n = -1 Check: |3(-1) + 2| - 5 = 4(-1) |3(-3) + 2| - 5 = 4(-3) |-3 + 2| - 5 = -4 |-9 + 2| - 5 = -12 |-1| - 5 = -4 |-7| - 5 = -12 1 - 5 = -4 7 - 5 = -12 ✔ -4 = -4 ✗ 2 = -12

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**What does absolute value mean?**

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