number theory - Simplifying Linear Congruences

I want to solve the given linear congruence

$$5x+1\equiv 2 \mod 6$$

My Approach:

$$\begin{align}&\Rightarrow& 5x -1&\equiv 0\mod 6 \\ &\Rightarrow& 6x -x-1&\equiv 0\mod6 \tag{ as $6\equiv 0\mod6$}\\ &\Rightarrow& 0 -x-1&\equiv 0\mod6 \\ &\Rightarrow& x&\equiv -1\mod 6 \end{align}$$

Am I correct till now ?? If I am correct, how to proceed further?