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}#.

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!