Solve for x |x-6|=9

$| x - 6 | = 9$

Step 1

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

$x - 6 = \pm 9$

Step 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.

$x - 6 = 9$

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

Add $6$ to both sides of the equation.

$x = 9 + 6$

Add $9$ and $6$ .

$x = 15$

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

$x - 6 = - 9$

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

Add $6$ to both sides of the equation.

$x = - 9 + 6$

Add $- 9$ and $6$ .

$x = - 3$

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

$x = 15, - 3$