Solve the Absolute Value Inequality for x |x/8|=3

$| \frac{x}{8} | = 3$

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

$\frac{x}{8} = \pm 3$

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.

$\frac{x}{8} = 3$

Multiply both sides of the equation by $8$ .

$8 \frac{x}{8} = 8 \cdot 3$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 \frac{x}{8} = 8 \cdot 3$

Rewrite the expression.

$x = 8 \cdot 3$

Simplify the right side.

Multiply $8$ by $3$ .

$x = 24$

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

$\frac{x}{8} = - 3$

Multiply both sides of the equation by $8$ .

$8 \frac{x}{8} = 8 \cdot - 3$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 \frac{x}{8} = 8 \cdot - 3$

Rewrite the expression.

$x = 8 \cdot - 3$

Simplify the right side.

Multiply $8$ by $- 3$ .

$x = - 24$

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

$x = 24, - 24$