Solve the Absolute Value Inequality for r |-2r-1|=11

$| - 2 r - 1 | = 11$

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

$- 2 r - 1 = \pm 11$

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.

$- 2 r - 1 = 11$

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

Add $1$ to both sides of the equation.

$- 2 r = 11 + 1$

Add $11$ and $1$ .

$- 2 r = 12$

Divide each term in $- 2 r = 12$ by $- 2$ and simplify.

Divide each term in $- 2 r = 12$ by $- 2$ .

$\frac{- 2 r}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 r}{- 2} = \frac{12}{- 2}$

Divide $r$ by $1$ .

$r = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$r = - 6$

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

$- 2 r - 1 = - 11$

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

Add $1$ to both sides of the equation.

$- 2 r = - 11 + 1$

Add $- 11$ and $1$ .

$- 2 r = - 10$

Divide each term in $- 2 r = - 10$ by $- 2$ and simplify.

Divide each term in $- 2 r = - 10$ by $- 2$ .

$\frac{- 2 r}{- 2} = \frac{- 10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 r}{- 2} = \frac{- 10}{- 2}$

Divide $r$ by $1$ .

$r = \frac{- 10}{- 2}$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$r = 5$

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

$r = - 6, 5$