jmc

If $n$ gives a remainder of 3 when divided by 7, then $n=7k+3$ for some integer $k$. Therefore, $2n+1=2(7k+3)+1=14k+6+1=14k+7=7(2k+1)$. Since $7(2k+1)$ is divisible by 7, the remainder when $2n+1$ is divided by 7 is $\boxed{0}$.