|x|=-5

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

x=±(-5)

Set up the positive portion of the ± solution.

x=-5

Set up the negative portion of the ± solution.

x=5

The solution to the equation includes both the positive and negative portions of the solution.

x=-5,5

Exclude the solutions that do not make |x|=-5 true.

No solution

Solve for x |x|=-5