# Solve absolute value inequality : 9<|4x+7|

Solve absolute value inequality : 9<|4x+7|
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Step 1
We first get rid of the absolute sign
9<4x+7 or, -9>4x+7
Step 2
Then we find x from each
9<4x+7
9-7<4x
2<4x
$\frac{2}{4}
$\frac{1}{2}
-9>4x+7
-9-7>4x
-16>4x
-4>x
Interval notation: $\left(-\mathrm{\infty },-4\right)\cup \left(\frac{1}{2},\mathrm{\infty }\right)$