$6x + 13 = 7 \pmod{24}$

Question

$6x + 13 = 7 \pmod{24}$

What method can I use to solve this problem?

I tried with the method I used here but it won't work because I can't use Euclidean algorithm on this problem.

Answer 1

Hint: $6x+13\equiv7\pmod{24}\iff6x\equiv-6\pmod{6\times4}$.

Answer 2

$x+2=4y+1$ by direct division by 6 when turned to linear polynomial form. Therefore, $x\equiv 3\bmod 4$

Answer 3

$$6x+13\equiv7\pmod{24}\iff 6x+6\equiv0\pmod{24}\iff 24|6x+6\iff 4|x+1$$