Another beginners calculus problem

Find an so that every fulfills

I've been brainstorming ideas, but it's a bit frustrating since I can't simplify the equation like I usually do.

Here are my thoughts and questions:

1) I'm thinking along the lines of proving something like because then I can simplify to . Is there any way I can make that happen?

2) Can ever be . Because if not, we know that must also be since the function must be .

3) Or can I just say M = 1000000000000, and since sinx is always between 1 and -1, it doesn't effect us, and 6x^2 is always bigger than 3x+1. so a x>M is definitely bigger than 1000.

Thanks!