Is squaring on both sides and solving a valid approach for dealing with problems with absolutes on both sides?

E.g.

|x - 3| = |2x - 4|

=>

(x-3)^2 = (2x-4)^2 and then solve for x?

Also, is it necessary to validate the solutions obtained by either methods (squaring, considering +ve/-ve cases), by plugging them into the original eqn?

I found the post which explains this clearly:
http://www.manhattangmat.com/forums/eivs-question-bank-q7-absolute-range-is-x-1-t2989.html

Looks like you helped yourself in the end!