Solve the Absolute Value Inequality for x |x/7|-8=-7

$| \frac{x}{7} | - 8 = - 7$

Move all terms not containing $| \frac{x}{7} |$ to the right side of the equation.

Add $8$ to both sides of the equation.

$| \frac{x}{7} | = - 7 + 8$

Add $- 7$ and $8$ .

$| \frac{x}{7} | = 1$

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

$\frac{x}{7} = \pm 1$

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.

$\frac{x}{7} = 1$

Multiply both sides of the equation by $7$ .

$7 \frac{x}{7} = 7 \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{x}{7} = 7 \cdot 1$

Rewrite the expression.

$x = 7 \cdot 1$

Simplify the right side.

Multiply $7$ by $1$ .

$x = 7$

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

$\frac{x}{7} = - 1$

Multiply both sides of the equation by $7$ .

$7 \frac{x}{7} = 7 \cdot - 1$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{x}{7} = 7 \cdot - 1$

Rewrite the expression.

$x = 7 \cdot - 1$

Simplify the right side.

Multiply $7$ by $- 1$ .

$x = - 7$

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

$x = 7, - 7$