While the mathematical explanation provided previously is always good to understand, remember that all the GMAT cares about is whether you can get to the right answer. When it comes to most absolute value questions, one should always try to plug-in the answer choices and/or pick numbers. The key is to know which numbers to pick in this case: -1, -1/2, 0, 1/2, 1, & 2; the same numbers; extreme numbers. In this case, one could pick x = -1/2 for each answer (except for B) to show that they do not have to be true. While this doesn't prove mathematically that B is correct, it does allow the other four answers to be eliminated. This is not a trick - in fact, its what the GMAT expects.
I hope this helps.
Any "thanks" would be greatly appreciated!
