Thanks for the wonderful help I've been getting!

Here is a problem with the Chinese Remainder Theorem:

x 1(mod 2)

x 2(mod 3)

x 3(mod 5)

x 4(mod 11)

x (1)(165) + (2)(110) + (3)(66) + (4)(30)

165 (mod 2) = 1

110 (mod 3) = 2

66 (mod 5) = 1

30 (mod 11) = 7 ??

I don't understand how the rest of the steps work if now we have to go back and use:

30 8 (mod 11) then 8 1 (mod 11)?

I thought I had finally comprehended Euclidean Algorithm with inverses, but now I'm not so sure.