Solve for x -1+|-9+x|=11

$- 1 + | - 9 + x | = 11$

Step 1

Move all terms not containing $| - 9 + x |$ to the right side of the equation.

Add $1$ to both sides of the equation.

$| - 9 + x | = 11 + 1$

Add $11$ and $1$ .

$| - 9 + x | = 12$

Step 2

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

$- 9 + x = \pm 12$

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.

$- 9 + x = 12$

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

Add $9$ to both sides of the equation.

$x = 12 + 9$

Add $12$ and $9$ .

$x = 21$

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

$- 9 + x = - 12$

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

Add $9$ to both sides of the equation.

$x = - 12 + 9$

Add $- 12$ and $9$ .

$x = - 3$

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

$x = 21, - 3$