Is it possible to play the sims 3 without a graphics card?

Well, you do have a graphics card... sort of....

Beginning with the 2nd generation Sandy Bridge CPU Intel has integrated a graphics core inside the CPU. Your CPU has the Intel HD 2000. It's good enough to do basic things like watching video, but when it comes to games it is not good at all. I think you found that out yourself.

Anyway, you need to buy a graphics card to play the Sims 3.