Your proof should start by explicitly stating the contrapositive of the claim. Did you do that? If not, do so.
Check your contrapositive here before proceeding further.
Are you stuck and just want to get this over with? You really want to peek at the full solution, right? Don't. You won't learn anything if you peek too early. First, try the these hints to help you get going.
When you have a proof written out, then look at the annotated solutions.