Find the value of x:

Question

20x ≡ 9 (mod 15)

Answer 1

Let x=1
20 ≡ 5 (mod 15)

As x increases by 1, the residue increases by 5, so no integer value of x satisfies the equation.

If you allow rational values for x, then it is easy to find many such x's: 9/20 comes to mind first...