Question

What is the extraneous solution of the given absolute value equation?
-2|-2x-4|=-12

Answer 1

9514 1404 393

Answer:

is no extraneous solution

Explanation:

An absolute value equation typically does not have extraneous solutions. The solutions to this one are ...

x ∈ {-5, 1}

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Unless there is some domain restriction, this equation has no extraneous solutions.

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For -2x-4 < 0

-2(2x +4) = -12

x +2 = 3

x = 1 . . . . . . -2(1)-4 = -6 < 0. Not an extraneous solution

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For -2x-4 > 0

-2(-2x -4) = -12

4x +8 = -12

4x = -20

x = -5 . . . . . . -2(-5) -4 = 6 > 0. Not an extraneous solution