Is it true that Iraq invaded Iran and Kuwait, then bombed both Saudi Arabia and Israel, before we invaded?

I remember Iran and Iraq had a war for about 10 years. I know that Bush, Sr. went to war with Iraq after they invaded Kuwait. I know that Israel was bombed during that war. I don't know about Saudi Arabia being bombed, as such....just off the top of my head. We could Google it, couldn't we? I'm a chimpanzee however.