$\displaystyle x - 3 > x + 2$

This could either become:

$\displaystyle = - x + 3 < x + 2$

$\displaystyle = 1 < 2x$

$\displaystyle = \tfrac{1}{2} < x$

OR:

$\displaystyle = x - 3 < -x -2$

$\displaystyle = 2x < 1$

$\displaystyle = x < \tfrac{1}{2} $

Why do these equations have different answers? What I did was change the side on one side of the equation, and solve for x.