A lot of absolutes

[Loki123]

So this problem has a lot of absolutes. I thought of a way to solve it and I ended up solving it correctly. However, is there an easier way to do this?

 

[Dr.Peterson]

The four boundary points -1, 0, 1, and 2 divide the number line into 5 regions. That gives 5 cases that must be solved (including each boundary point in one neighboring region). I see nothing shorter than that. So you have done just a little more work than needed, in your awkward way of finding cases, and your one extra case.