If $n$ gives a remainder of 3 when divided by 7, then what remainder does $2n+1$ give when divided by 7?
I want to find the remainder of $2n+1$ when divided by 7, but I don't know the exact value of $n$. However, I do know that $n$ has a remainder of 3 when divided by 7, so I can write $n$ as $7k+3$ for some integer $k$. Now I can substitute $7k+3$ for $n$ in the expression $2n+1$ and simplify: $2n+1 = 2(7k+3)+1 = 14k+7$. I see that $14k+7$ is divisible by 7, so it has a remainder of 0 when divided by 7. Therefore, the answer is 0. 