# How do you solve and graph  |2x + 1| > -3?

Mar 10, 2018

$x > - 2 \mathmr{and} x < 1$

#### Explanation:

$| 2 x + 1 | > - 3$

Solve for the absolute value

We know either: $2 x + 1 > - 3 \mathmr{and} 2 x + 1 < - \left(- 3\right)$

Now let's solve the first possibility which is $2 x + 1 > - 3$

$2 x + 1 > - 3$

Add $- 1$ on both sides

$2 x + 1 - 1 > - 3 - 1$

$2 x > - 4$

Divide both sides by $2$

$\frac{2 x}{2} > \frac{- 4}{2}$

$x > - 2$

Now let's solve the second possibility

$2 x + 1 < - \left(- 3\right)$

$2 x + 1 < 3$

Add $- 1$ on both sides

$2 x + 1 - 1 < 3 - 1$

$2 x < 2$

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

$x < 1$

Thus,

$x > - 2 \mathmr{and} x < 1$