# How do you solve -7abs(-3-3r)=-21?

Aug 25, 2016

The solution set is $\left\{0 , - 2\right\}$.

#### Explanation:

Let's first isolate the absolute value on one side of the equation.

$| - 3 - 3 r | = - \frac{21}{-} 7$

$| - 3 - 3 r | = 3$

Now, when dealing with absolute value equations, we must consider two scenarios.

A: The absolute value is positive.

$- 3 - 3 r = 3$

$- 3 r = 6$

$r = - 2$

B: The absolute value is negative

$- \left(- 3 - 3 r\right) = 3$

$3 + 3 r = 3$

$3 r = 0$

$r = 0$

The solutions are $r = 0 \mathmr{and} r = - 2$. However, let's check that the solutions satisfy the original equation before stating the solution set.

-7|-3 - 3(0)| =^? -21

-7|-3| =^? -21

$- 7 \left(3\right) = - 21$

AND

-7|-3 - (-3 xx -2)| =^? -21

-7|3| =^? -21

$- 7 \left(3\right) = - 21$

Hence, neither of the solutions are extraneous. The solution set is $\left\{0 , - 2\right\}$.

Hopefully this helps!