I was given a rate of pay before I interviewed for...

I was given a rate of pay before I interviewed for a position, which I agreed upon. After the client made an offer, 3i People tried to offer me $7 less. I had to negotiate to get a higher rate, but it was not what was offered in the initial email. Even though I provided 3i with the email stating the amount, they still what not rectify the issue. Because this was not the clients problem and I really wanted the job, I went ahead and accepted the offer at a lower rate with the hopes of being hired on at a higher rate.