Solve the Absolute Value Inequality for x |x/2-4|=2

$| \frac{x}{2} - 4 | = 2$

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

$\frac{x}{2} - 4 = \pm 2$

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.

$\frac{x}{2} - 4 = 2$

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

Add $4$ to both sides of the equation.

$\frac{x}{2} = 2 + 4$

Add $2$ and $4$ .

$\frac{x}{2} = 6$

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 6$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 6$

Rewrite the expression.

$x = 2 \cdot 6$

Simplify the right side.

Multiply $2$ by $6$ .

$x = 12$

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

$\frac{x}{2} - 4 = - 2$

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

Add $4$ to both sides of the equation.

$\frac{x}{2} = - 2 + 4$

Add $- 2$ and $4$ .

$\frac{x}{2} = 2$

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 2$

Rewrite the expression.

$x = 2 \cdot 2$

Simplify the right side.

Multiply $2$ by $2$ .

$x = 4$

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

$x = 12, 4$