Solve for x |x+2|-3=7

$| x + 2 | - 3 = 7$

Step 1

Move all terms not containing $| x + 2 |$ to the right side of the equation.

Add $3$ to both sides of the equation.

$| x + 2 | = 7 + 3$

Add $7$ and $3$ .

$| x + 2 | = 10$

Step 2

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

$x + 2 = \pm 10$

Step 3

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.

$x + 2 = 10$

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

Subtract $2$ from both sides of the equation.

$x = 10 - 2$

Subtract $2$ from $10$ .

$x = 8$

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

$x + 2 = - 10$

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

Subtract $2$ from both sides of the equation.

$x = - 10 - 2$

Subtract $2$ from $- 10$ .

$x = - 12$

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

$x = 8, - 12$