Solve the Absolute Value Inequality for x |x-12|-3=11

$| x - 12 | - 3 = 11$

Step 1

Move all terms not containing $| x - 12 |$ to the right side of the equation.

Add $3$ to both sides of the equation.

$| x - 12 | = 11 + 3$

Add $11$ and $3$ .

$| x - 12 | = 14$

Step 2

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

$x - 12 = \pm 14$

Step 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.

$x - 12 = 14$

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

Add $12$ to both sides of the equation.

$x = 14 + 12$

Add $14$ and $12$ .

$x = 26$

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

$x - 12 = - 14$

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

Add $12$ to both sides of the equation.

$x = - 14 + 12$

Add $- 14$ and $12$ .

$x = - 2$

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

$x = 26, - 2$