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How do you solve #x/3+2=x/2-1# and check for extraneous solutions?

Answer 1

Isaiah Anthony

#x=18#

Multiplying the equation by #6# we get #2x+12=3x-6# adding #6# and subtracting #2x# we get #18=x#

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Answer 2

Eva Abramson

To solve the equation x/3 + 2 = x/2 - 1:

Multiply every term by the least common denominator (LCD) to clear the fractions.
Simplify the resulting equation to isolate the variable x.
Check the solutions obtained by plugging them back into the original equation to ensure they are not extraneous.

The solution to the equation is x = 12. Checking this solution, we find that it is not extraneous.

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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.