Solve the Absolute Value Inequality for r |-3r|=9

$| - 3 r | = 9$

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

$- 3 r = \pm 9$

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.

$- 3 r = 9$

Divide each term in $- 3 r = 9$ by $- 3$ and simplify.

Divide each term in $- 3 r = 9$ by $- 3$ .

$\frac{- 3 r}{- 3} = \frac{9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 r}{- 3} = \frac{9}{- 3}$

Divide $r$ by $1$ .

$r = \frac{9}{- 3}$

Simplify the right side.

Divide $9$ by $- 3$ .

$r = - 3$

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

$- 3 r = - 9$

Divide each term in $- 3 r = - 9$ by $- 3$ and simplify.

Divide each term in $- 3 r = - 9$ by $- 3$ .

$\frac{- 3 r}{- 3} = \frac{- 9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 r}{- 3} = \frac{- 9}{- 3}$

Divide $r$ by $1$ .

$r = \frac{- 9}{- 3}$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$r = 3$

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

$r = - 3, 3$