elementary number theory - Solving Congruence Equations Bbb Z_11

I have an equation $$6 \pmod {11} x = 3 \pmod{11}$$

and I need to find the variable x which solve the equation.
I found that $x=6$ by trying $x=0,1,2,3,4,5$.

Before, posing this question, I made a search here and in youtube and found the way which described above: https://www.youtube.com/watch?v=U9Eo6Bsvm4M.

That`s an easy equation but the question is how can I find the variable without try all the options?