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.

Subtract $3$ from both sides of the equation.

$x = 7 - 3$

Subtract $3$ from $7$ .

$x = 4$

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.

Subtract $3$ from both sides of the equation.

$x = - 7 - 3$

Subtract $3$ from $- 7$ .

$x = - 10$

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

$x = 4, - 10$