Epsilon-proof as x->-infinity currently defeating me

I think Epsilon-delta proofs and I should spend some quality time together.

The problem is I need to prove that:

So, I need to show that, for every , there is a such that whenever .

So, given , I need to find such that:

whenever

And here's where I am stuck. I think I'll have to take a log in there somewhere. Wish my textbook wasn't so scarce on examples (Stewart's Calculus 4th edition). I sort of get limits where x->c, but I'm totally lost on the ones with infinities, and the differences between handling + and - infinities. Can't find any examples online of ones as x-> -infinity, which surely might help. Nor are the two videos at Khan Academy useful in this case.

I bet you guys get a lot of these. Surprisingly confusing for what seems a relatively simple concept, at first. Help, hints, pointers, nudges and taunts all appreciated.