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How do you solve the equation and identify any extraneous solutions for #abs(x-2)=6x+18#?

Answer 1

Hazel Anglin

Verify those numbers!

#x - 2 = 6x + 18 or 2 - x = 6x + 18#

#- 20 = 5x or -16 = 7x#

#- 4 = x or -16/7 = x#

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Answer 2

Julia Adams

To solve the equation ( |x - 2| = 6x + 18 ) and identify any extraneous solutions:

Solve the equation ( |x - 2| = 6x + 18 ).
Split the equation into two cases: a) ( x - 2 = 6x + 18 ) b) ( -(x - 2) = 6x + 18 )
Solve each case separately.
Check each solution to see if it satisfies the original equation.
Identify any solutions that do not satisfy the original equation as extraneous.

The solutions are the intersection of the solutions for both cases.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.