Solve for x 1+|2+x|=9

$1 + | 2 + x | = 9$

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

Subtract $1$ from both sides of the equation.

$| 2 + x | = 9 - 1$

Subtract $1$ from $9$ .

$| 2 + x | = 8$

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

$2 + x = \pm 8$

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.

$2 + x = 8$

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

Subtract $2$ from both sides of the equation.

$x = 8 - 2$

Subtract $2$ from $8$ .

$x = 6$

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

$2 + x = - 8$

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

Subtract $2$ from both sides of the equation.

$x = - 8 - 2$

Subtract $2$ from $- 8$ .

$x = - 10$

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

$x = 6, - 10$