Solve 7x = 11 mod 9 by finding an inverse for 7. (= is congruence not equality)

I'm trying to do this by using the euclidean algorithm:

9 = 1(7) + 2

7 = 2(3) + 1

3 = 1(3) + 0

If have done the above correctly, How do I use this to find the inverse of 7?

Thanks.