# How do you solve abs(-2x -5) + 2 > 9?

Mar 16, 2018

The solution set $S = \left\{x \in \mathbb{R} | \left(x < - 6\right) \mathmr{and} \left(x > 2\right)\right\}$

#### Explanation:

First let's clean up:

$\left\mid - 2 x - 5 \right\mid > 7$

We have to distinguish two cases:

(1) $\left(- 2 x - 5\right) > 7$ which is obvious ;-)

and

(2) $\left(- 2 x - 5\right) < - 7$ which is true, because the absolute of a nuber $< - 7$ is $> 7$.

Lets solve case (1) with some cleanup:

$- 2 x - 5 > 7$

$- 2 x > 12$

$x < - 6$

and case (2) results as follows:

$- 2 x - 5 < - 7$

$- 2 x < - 2$

$x > 2$

The solution set $S = \left\{x \in \mathbb{R} | \left(x < - 6\right) \mathmr{and} \left(x > 2\right)\right\}$