I just realised that I made it an equation rather then an inequality. that's supposed to be

But I solved it

I eventually observed that

You then get

Move the negative terms over and that gives the simplified version of what I wanted to prove.

divide that by 2

then add to both sides

Since

We can write

Divide that again by 2 and you get

Sorry about that. It's just hard catching all my tex mistakes right away.