# How do you solve abs(x-2)>x+4?

Jul 2, 2018

The solution is $x \in \left(- \infty , - 1\right)$

#### Explanation:

This is solving an inequality with absolute values.

$x - 2 = 0$, $\implies$, $x = 2$

There are $2$ intervals to consider

$\left(- \infty , 2\right)$ and $\left(2 , + \infty\right)$

In the Interval $\left(- \infty , 2\right)$

$- x + 2 > x + 4$

$\implies$, $2 x < - 2$

$\implies$, $x < - 1$

As $x < - 1$ $\in$ the interval, the solution is accepted

In the Interval $\left(2 , + \infty\right)$

$x - 2 > x + 4$

$\implies$, $0 > 6$

There is no solution in the interval.

The solution is $x \in \left(- \infty , - 1\right)$

graph{|x-2|-x-4 [-18.01, 18.02, -9, 9.01]}