1. Absolute Value Inequality
Solve & Graph
Absolute Value Inequality

2. 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.

3. 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

4. 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

5. What does absolute value mean?