# How do you solve the inequality:  abs(x + 2) < 18?

##### 1 Answer
Aug 27, 2015

$x < 16$
$x > - 20$

#### Explanation:

$\left\mid x + 2 \right\mid < 18$

Separate the inequality into two inequalities, one positive and one negative.

$x + 2 < 18 \mathmr{and} - \left(x + 2\right) < 18$

Positive Inequality

$x + 2 < 18$

Subtract $2$ from both sides.

$x < 18 - 2$$=$

$x < 16$

Negative Inequality

$- \left(x + 2\right) < 18$

$- x - 2 < 18$

Add $2$ to both sides.

$- x < 18 + 2$$=$

$- x < 20$

Multiply both sides times $- 1$.

$x > - 20$

Solutions for $x$.

$x < 16$
$x > - 20$