Solve for x |x-7|=4

$| x - 7 | = 4$

Step 1

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

$x - 7 = \pm 4$

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.

$x - 7 = 4$

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

Add $7$ to both sides of the equation.

$x = 4 + 7$

Add $4$ and $7$ .

$x = 11$

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

$x - 7 = - 4$

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

Add $7$ to both sides of the equation.

$x = - 4 + 7$

Add $- 4$ and $7$ .

$x = 3$

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

$x = 11, 3$