I just broke up with my ex bf. I wanna know if my reason of leaving him is worth the break up.?

I'm turning 21 dis year and he's 44. I always had problems trusting him. I cheated on him bfor bcoz of my frustrations in d kind of relationship dat we hav. Til I got to my senses nd dcided to jst stick in d relationship. In other words I wnted him to b my last. No matter how hard I tried though, I jst cudn't trust him. He lied to me a lot of tyms. I caught him in sum dating sites nd luking at nude pics of girls on d internet whyl we wer stil living together. So i've dcided to move out nd live wit my aunt in a diff. state 3 hrs away from him. We nver lost communication. We talked over d phone nd sent emails everyday to each other. He always tells me he loves me nd dat he cnt wait until I get back. I knw to myslf that I'm coming home to him again til one nyt I snooped on his email acct. I guesd for d psword nd it opend it to my surprise. I saw dat he's on dis dating site. I went der nd saw dat he's online and chatting called him nd broke up. Am I ryt with my reasons to breakup? Pls help