1) Let's look at the left side. For any 'x', only that middle term will have any influence as far as producing a negative number. However, the other two terms contribute three times the influence to the positive. In other words, it's safe to say that this thing is NEVER negative.
2) Still on the right side -- For x > 1, ALL THREE TERMS are positive so we can just chuck the Absolute Values, giving 2x-1
3) Looking at the right side: Hey! That has the same slope and the same y-intercept. There aremany solutions to this guy.
This kind of thinking can be done rather quickly. You are right - you don't have time for a formal examination in the middle of the GRE, but you may be able to spot something useful with a little creative thinking.