Solve the Absolute Value Inequality for x 8=|5-x|

$8 = | 5 - x |$

Rewrite the equation as $| 5 - x | = 8$ .

$| 5 - x | = 8$

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

$5 - x = \pm 8$

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.

$5 - x = 8$

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

Subtract $5$ from both sides of the equation.

$- x = 8 - 5$

Subtract $5$ from $8$ .

$- x = 3$

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 $- 1$ .

$x = - 3$

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

$5 - x = - 8$

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

Subtract $5$ from both sides of the equation.

$- x = - 8 - 5$

Subtract $5$ from $- 8$ .

$- x = - 13$

Divide each term in $- x = - 13$ by $- 1$ and simplify.

Divide each term in $- x = - 13$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 13}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 13}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 13}{- 1}$

Simplify the right side.

Divide $- 13$ by $- 1$ .

$x = 13$

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

$x = - 3, 13$