Solve for y 13=|11-y|

$13 = | 11 - y |$

Rewrite the equation as $| 11 - y | = 13$ .

$| 11 - y | = 13$

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

$11 - y = \pm 13$

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.

$11 - y = 13$

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

Subtract $11$ from both sides of the equation.

$- y = 13 - 11$

Subtract $11$ from $13$ .

$- y = 2$

Divide each term in $- y = 2$ by $- 1$ and simplify.

Divide each term in $- y = 2$ by $- 1$ .

$\frac{- y}{- 1} = \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{2}{- 1}$

Divide $y$ by $1$ .

$y = \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$y = - 2$

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

$11 - y = - 13$

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

Subtract $11$ from both sides of the equation.

$- y = - 13 - 11$

Subtract $11$ from $- 13$ .

$- y = - 24$

Divide each term in $- y = - 24$ by $- 1$ and simplify.

Divide each term in $- y = - 24$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 24}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 24}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 24}{- 1}$

Simplify the right side.

Divide $- 24$ by $- 1$ .

$y = 24$

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

$y = - 2, 24$