Solve for x |-8x|=8

$| - 8 x | = 8$

Step 1

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

$- 8 x = \pm 8$

Step 2

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.

$- 8 x = 8$

Divide each term in $- 8 x = 8$ by $- 8$ and simplify.

Divide each term in $- 8 x = 8$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{8}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{8}{- 8}$

Divide $x$ by $1$ .

$x = \frac{8}{- 8}$

Simplify the right side.

Divide $8$ by $- 8$ .

$x = - 1$

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

$- 8 x = - 8$

Divide each term in $- 8 x = - 8$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 8$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 8}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 8}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 8}$

Simplify the right side.

Divide $- 8$ by $- 8$ .

$x = 1$

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

$x = - 1, 1$