Solve the Absolute Value Inequality for x 2=|x|-1

$2 = | x | - 1$

Step 1

Rewrite the equation as $| x | - 1 = 2$ .

$| x | - 1 = 2$

Step 2

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

Add $1$ to both sides of the equation.

$| x | = 2 + 1$

Add $2$ and $1$ .

$| x | = 3$

Step 3

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

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$