Solve for x |x|-2=3

$| x | - 2 = 3$

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

Add $2$ to both sides of the equation.

$| x | = 3 + 2$

Add $3$ and $2$ .

$| x | = 5$

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

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$