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

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

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Answer 1 · 2016-08-25T01:56:16

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

Explanation:

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

$|-3 - 3r| = -21/-7$

$|-3 - 3r| = 3$

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

A: The absolute value is positive.

$-3 - 3r = 3$

$-3r = 6$

$r = -2$

B: The absolute value is negative

$-(-3 - 3r) = 3$

$3 + 3r = 3$

$3r = 0$

$r = 0$

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

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

$-7|-3| =^? -21$

$-7(3) = -21$

AND

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

$-7|3| =^? -21$

$-7(3) = -21$

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

Hopefully this helps!

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