Solve 3x + 3 = x + 5 mod 11 (= is congruence not equality...)
(3x - x) = (5 - 3) mod 11
2x = 2 mod 11
2x = 13 mod 11
x = 13/2 mod 11
Is this correct?
No. To be able to divide by an element $\displaystyle a$ (2 in this example) you need to find $\displaystyle a^{-1}$ such that $\displaystyle a\times a^{-1}=1$. If the inverse does not exist, you cannot "divide" by $\displaystyle a$.
so in your example, $\displaystyle a=2$ and $\displaystyle a^{-1}=6$ ...