# How do you solve abs(-2x+4)=6?

Apr 3, 2015

There are 2 possibilities $x < 2$ and $x > 2$ (we can ignore the possible third possibility $x = 2$ by inspection).

If $x < 2$ then $\left(- 2 x + 4\right)$ is positive and
$\left\mid - 2 x + 4 \right\mid = \left(- 2 x + 4\right)$
In which case
$- 2 x + 4 = 6$
$x = - 1$

If $x > 2$ then $\left(- 2 x + 4\right)$ is negative and
$\left\mid - 2 x + 4 \right\mid = 2 x - 4$
in which case
$2 x - 4 = 6$
$x = 5$

$x = - 1$
or
$x = 5$