# How do you solve and graph -5 < 2x + 1 < 4?

May 2, 2018

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

Shade the area between a dashed line for $x = - 3$ and a dashed line for $x = \frac{3}{2}$

#### Explanation:

We want just $x$ on its own in the middle.

First,we take away 1 from both sides:

$- 5 - 1 < 2 x + 1 - 1 < 4 - 1$
$- 6 < 2 x < 3$

Then divide all terms by $2$:

$- \frac{6}{2} < \frac{2 x}{2} < \frac{3}{2}$
$- 3 < x < \frac{3}{2}$

To graph the inequality, draw a dashed line for $x = - 3$ and $x = \frac{3}{2}$ and shade between the two lines.