Solve the Absolute Value Inequality for x |x-3|=7

$| x - 3 | = 7$

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

$x - 3 = \pm 7$

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.

$x - 3 = 7$

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

Add $3$ to both sides of the equation.

$x = 7 + 3$

Add $7$ and $3$ .

$x = 10$

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

$x - 3 = - 7$

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

Add $3$ to both sides of the equation.

$x = - 7 + 3$

Add $- 7$ and $3$ .

$x = - 4$

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

$x = 10, - 4$