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

1 Answer
Noah G
Aug 25, 2016

The solution set is {0, -2}{0,−2}.

Explanation:

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

|-3 - 3r| = -21/-7|−3−3r|=−21−7

|-3 - 3r| = 3|−3−3r|=3

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

A: The absolute value is positive.

-3 - 3r = 3−3−3r=3

-3r = 6−3r=6

r = -2r=−2

B: The absolute value is negative

-(-3 - 3r) = 3−(−3−3r)=3

3 + 3r = 33+3r=3

3r = 03r=0

r = 0r=0

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

-7|-3 - 3(0)| =^? -21−7|−3−3(0)|=?−21

-7|-3| =^? -21−7|−3|=?−21

-7(3) = -21−7(3)=−21

AND

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

-7|3| =^? -21−7|3|=?−21

-7(3) = -21−7(3)=−21

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

Hopefully this helps!

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