# How do you solve |5x + \frac{1}{2} | - 4< 3?

Sep 20, 2016

$- \frac{3}{2} < x < \frac{13}{10}$

#### Explanation:

We have: $\left\mid 5 x + \frac{1}{2} \right\mid - 4 < 3$

First, let's add $4$ to both sides of the inequality:

$\implies \left\mid 5 x + \frac{1}{2} \right\mid < 7$

Then, we will split the inequality into two parts:

$\implies 5 x + \frac{1}{2} < 7$

$\implies 5 x < \frac{13}{2}$

$\implies x < \frac{13}{10}$

or

$\implies 5 x + \frac{1}{2} > - 7$

$\implies 5 x > - \frac{15}{2}$

$\implies x > - \frac{3}{2}$

Therefore, the solution set to this inequality is $- \frac{3}{2} < x < \frac{13}{10}$.