Absolute Value EQ w/ Fraction

It doesn't seem especially tough but there's not an example in the book and it was on a quiz today. Please note that I did consult the Inequality sticky at the top of the forum but I didn't see one quite like this. I apologize in advance if I missed it.

My first thought was to multiply everything by the denominator 3 so that:

Then: add 3 to 6 so that:

Then: divide by 3 so that:

Then: add 1 to both sides so that:

So that...

x is equal to +2 and x is equal to -2

It seemed tidy enough at the time but I have a feeling it's wrong; that maybe I should multiplied 2x-1 by 3 at some point or that I'm remiss in some way or another. Any and all help is appreciated. Thanks.

Re: Absolute Value EQ w/ Fraction

Quote:

Originally Posted by

**Trypanosoma**

Simply note that

Re: Absolute Value EQ w/ Fraction

Re: Absolute Value EQ w/ Fraction

Quote:

Originally Posted by

**Trypanosoma** A Picard facepalm moment for me... I've also noticed that not multiplying -1 or 2 that my answer still comes out to same. Will that stand up for precisely similar problems?

But what of something like.

I in no way suggested that your solution is wrong.

I just wanted to point that it was awkward.

You should know that .

So your problem quickly simplifies to .

Thus