Solve the Absolute Value Inequality for r -2|-2r-4|=-12

$- 2 | - 2 r - 4 | = - 12$

Step 1

Divide each term in $- 2 | - 2 r - 4 | = - 12$ by $- 2$ and simplify.

Divide each term in $- 2 | - 2 r - 4 | = - 12$ by $- 2$ .

$\frac{- 2 | - 2 r - 4 |}{- 2} = \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 | - 2 r - 4 |}{- 2} = \frac{- 12}{- 2}$

Divide $| - 2 r - 4 |$ by $1$ .

$| - 2 r - 4 | = \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$| - 2 r - 4 | = 6$

Step 2

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

$- 2 r - 4 = \pm 6$

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.

$- 2 r - 4 = 6$

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

Add $4$ to both sides of the equation.

$- 2 r = 6 + 4$

Add $6$ and $4$ .

$- 2 r = 10$

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 $- 2$ .

$r = - 5$

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

$- 2 r - 4 = - 6$

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

Add $4$ to both sides of the equation.

$- 2 r = - 6 + 4$

Add $- 6$ and $4$ .

$- 2 r = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $r$ by $1$ .

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

Simplify the right side.

Divide $- 2$ by $- 2$ .

$r = 1$

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

$r = - 5, 1$

Solve the Absolute Value Inequality for r -2|-2r-4|=-12

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