# How do you graph and solve 2x-abs[x+4]> 8?

Oct 27, 2017

$x > 12$

#### Explanation:

$2 x - \left\mid x + 4 \right\mid = 8 + {\epsilon}^{2}$ with $\epsilon \ne 0$ or

$2 x - 8 - {\epsilon}^{2} = \left\mid x + 4 \right\mid$ or

${\left(2 x - 8 - {\epsilon}^{2}\right)}^{2} - {\left(x + 4\right)}^{2} = 0$ or

$\left(- {\epsilon}^{2} - 12 + x\right) \left(- {\epsilon}^{2} - 4 + 3 x\right) = 0$ or

$\left\{\begin{matrix}- {\epsilon}^{2} - 12 + x = 0 \\ - {\epsilon}^{2} - 4 + 3 x = 0\end{matrix}\right.$

or

$\left\{\begin{matrix}x > 12 \\ x > \frac{4}{3}\end{matrix}\right.$

and the solution is $x > 12$