Solve the Absolute Value Inequality for x 4-|x|=1

$4 - | x | = 1$

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

Subtract $4$ from both sides of the equation.

$- | x | = 1 - 4$

Subtract $4$ from $1$ .

$- | x | = - 3$

Divide each term in $- | x | = - 3$ by $- 1$ and simplify.

Divide each term in $- | x | = - 3$ by $- 1$ .

$\frac{- | x |}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{| x |}{1} = \frac{- 3}{- 1}$

Divide $| x |$ by $1$ .

$| x | = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$| x | = 3$

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

$x = \pm 3$

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.

$x = 3, - 3$