# Solve absolute value inequality. |2x-6|<8

Solve absolute value inequality.
|2x-6|<8
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Laura Worden
Step 1
Given inequality,
|2x-6|<8
Step 2
Simplification:
We know that,
|u|<a then -a < u<a
So
|2x-6|<8
-8<2x-6 <8
-8+6<2x-6+6<8+6
-2<2x<14
$-\frac{2}{2}<\frac{2x}{2}<\frac{14}{2}$
-1<x<7
Step 3
Hence,
-1

zurilomk4
Step 1
First we add 6 and then divide by 2
|2x-6|<8
-8<2x-6 <8
-8+6 < 2x<8+6
-2<2x<14
-1<x<7
Step 2