Solve for x |x+2|+6=11

$| x + 2 | + 6 = 11$

Step 1

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

Subtract $6$ from both sides of the equation.

$| x + 2 | = 11 - 6$

Subtract $6$ from $11$ .

$| x + 2 | = 5$

Step 2

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

$x + 2 = \pm 5$

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.

$x + 2 = 5$

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

Subtract $2$ from both sides of the equation.

$x = 5 - 2$

Subtract $2$ from $5$ .

$x = 3$

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

$x + 2 = - 5$

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

Subtract $2$ from both sides of the equation.

$x = - 5 - 2$

Subtract $2$ from $- 5$ .

$x = - 7$

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

$x = 3, - 7$