# How do you solve abs [x]= 2x +6?

Apr 27, 2017

$x = - 2$

#### Explanation:

We can split up the absolute value into two functions
$x = 2 x + 6$
$- x = 2 x + 6$

Solving for $x$ in the first equation we get the following
$- x = 6$
$x = - 6$

Solving for the second equation we get the following
$- 3 x = 6$
$x = - 2$

We need to plug the values into the function to make sure all the answers we got satisfy the conditions.
$x = - 6$
$\setminus \left\mid - 6 \right\mid = 2 \left(- 6\right) + 6$
$6 = - 12 + 6$
$6 \setminus \ne - 6$
So we know $x = - 6$ is not a solution.

$x = - 2$
$\setminus \left\mid - 2 \right\mid = 2 \left(- 2\right) + 6$
$2 = - 4 + 6$
$2 = 2$
So $x = - 2$ is a solution.