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.

$\displaystyle 3 \mid \frac{\2x-1}{3}\mid -1 \geq2$

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

$\displaystyle 3\mid \2x-1\mid -3 \geq6$ Then: add 3 to 6 so that:

$\displaystyle 3\mid \2x-1\mid \geq9$ Then: divide by 3 so that:

$\displaystyle 2x-1\geq3$ Then: add 1 to both sides so that:

$\displaystyle 2x\geq4$ 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.