Solve for x |x-5|=7

$| x - 5 | = 7$

Step 1

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

$x - 5 = \pm 7$

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.

$x - 5 = 7$

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

Add $5$ to both sides of the equation.

$x = 7 + 5$

Add $7$ and $5$ .

$x = 12$

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

$x - 5 = - 7$

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

Add $5$ to both sides of the equation.

$x = - 7 + 5$

Add $- 7$ and $5$ .

$x = - 2$

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

$x = 12, - 2$