# How do you solve and graph |-2x + 4| > 6?

Aug 29, 2017

$x < - 1 ,$$x > 5$

Refer to the explanation for the process and the graph.

#### Explanation:

Given:

$\left\mid - 2 x + 4 \right\mid > 6$

Since $\left\mid a \right\mid = \pm a$, the inequality can be broken down into two: one positive and one negative.

$- 2 x + 4 > 6 \textcolor{w h i t e}{\ldots}$and$\textcolor{w h i t e}{\ldots} - \left(2 x + 4\right) > 6$

Positive Inequality

$- 2 x + 4 > 6$

Subtract $4$ from both sides.

$- 2 x > 6 - 4$

Simplify.

$- 2 x > 2$

Divide both sides by $- 2$. This will reverse the inequality.

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

$x < - 1$

Negative Inequality

$- \left(- 2 x + 4\right) > 6$

Simplify.

$2 x - 4 > 6$

Add $4$ to both sides.

$2 x > 6 + 4$

Simplify.

$2 x > 10$

Divide both sides by $2$.

$x > 5$

Solutions:

$x < - 1$

$x > 5$

Graph

The dots for $- 1$ and $5$ are not filled in because they are not part of the inequality.