Okay, after going through it carefully I completely understand the way you're supposed to think it out and am surprised I didn't see it. I was just too busy thinking in terms of equations and knowing algebra, which isn't really what the PSAT is about.
Of course, I still don't know how I arrived at the wrong conclusion with my original work. It appeared to be giving me the opposite answers of what it really was. What is the method for solving an inequality like this? Are you supposed to flip the sign when you're done?