The mistake of this problem lies in the step of "dividing both sides by x" because in this problem, x is unknown, and we can't guarantee that x≠0. The theorem "Two sides of an equation are divided by a certain number at the same time, and both sides of the equation still hold" requires that the divisor is not 0, so we can't divide by both sides of the equation at the same time until we know whether X is 0 or not.

The correct answer to this question should be this:

Starting from 2x=3x and subtracting 2x from both sides at the same time, we get:

0=x

Move x to the left to get:

-x=0

Divide both sides by-1 to get:

x=0