Solve the inequality x<y<0?

You can really solve it as such but you can represent it on a graph. You know y<0 so y can only have negative values. x<y so x can also only have negative values and negative values less than y. If you plot a line for x=y and stop it at x=0 (or y=0, because x=y), then shade the bit above it where y>x, you'll have what x<y<0 looks like.

I've drawn it for you:

http://imgur.com/jCdcBjH

The bit I shaded blue is what I mean.