Double sided modulus equation: $|2x-1| = |3x+2|$ Considering this equation $$|2x-1| = |3x+2|$$
My question is what is the reasoning behind taking only the positive and negative values of one side of the equation to solve the problem. I have seen many people do that and it seems to work. 
For e.g., $$2x-1 = 3x+2$$ 
          $$2x-1 = -(3x+2),$$ 
then solve for $x$.On the other hand, I have been taught that I should be testing both positive and negative values on both sides which will eventually give 4 cases to solve instead of 2. This makes more sense since disregarding the absolute value sign give rise to the situation, a negative and positive value.

There are actually just two cases. Case I:
$$2x - 1 = 3x + 2$$
yields $x = -3$.
Now for case II:
$$2x - 1 = -3x - 2$$
yields $x = -1/5$.
No quadradic machinery required.
