Finding Integers Based on Modular Arithmetic

Let $n$ be an integer such that $5n + 7$ is a multiple of 3. Which of the following integers can $n$ be?

To determine this, we need to consider the expression $5n + 7$ modulo 3. This boils down to checking the possible values of $n$ and seeing if $5n + 7 mod{3} = 0$.