Solve for x |x-4|=7

$| x - 4 | = 7$

Step 1

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

$x - 4 = \pm 7$

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.

$x - 4 = 7$

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

Add $4$ to both sides of the equation.

$x = 7 + 4$

Add $7$ and $4$ .

$x = 11$

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

$x - 4 = - 7$

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

Add $4$ to both sides of the equation.

$x = - 7 + 4$

Add $- 7$ and $4$ .

$x = - 3$

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

$x = 11, - 3$