Solve for x 6=|x|-2

$6 = | x | - 2$

Step 1

Rewrite the equation as $| x | - 2 = 6$ .

$| x | - 2 = 6$

Step 2

Move all terms not containing $| x |$ to the right side of the equation.

Add $2$ to both sides of the equation.

$| x | = 6 + 2$

Add $6$ and $2$ .

$| x | = 8$

Step 3

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x = \pm 8$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 8$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 8$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 8, - 8$