Solve the Absolute Value Inequality for x 2|x-2|-12=0

$2 | x - 2 | - 12 = 0$

Add $12$ to both sides of the equation.

$2 | x - 2 | = 12$

Divide each term in $2 | x - 2 | = 12$ by $2$ and simplify.

Divide each term in $2 | x - 2 | = 12$ by $2$ .

$\frac{2 | x - 2 |}{2} = \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | x - 2 |}{2} = \frac{12}{2}$

Divide $| x - 2 |$ by $1$ .

$| x - 2 | = \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$| x - 2 | = 6$

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

$x - 2 = \pm 6$

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.

$x - 2 = 6$

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

Add $2$ to both sides of the equation.

$x = 6 + 2$

Add $6$ and $2$ .

$x = 8$

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

$x - 2 = - 6$

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

Add $2$ to both sides of the equation.

$x = - 6 + 2$

Add $- 6$ and $2$ .

$x = - 4$

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

$x = 8, - 4$