Proof: If $x$ is odd, then $x+2$ is odd. I'm fairly new to writing proofs so any advice can help. 
I'm asked to prove the following statement: "If $x$ is odd, then $x+2$ is odd". Here is my proof: 
We will prove this by contraposition: if $x+2$ is not odd, then $x$ is not odd. 
Let there be an integer $k$ such that $x+2 = 2k$.
Thus,
\begin{align}
x & = 2k-2 \\
 & = 2(k-1)
\end{align}
Then $x = 2(k-1)$ is an even number. 
Since the contrapositive is true, the statement "If $x$ is odd, then $x+2$ is odd" is true by logical equivalency. 

The problem is: I don't know if my proof is enough or how to properly tackle them. Any advice? 

This seems fine as long as you know that "not odd" is the same as even for integers. Also, for your opening sentence in the proof, I might say "If $x+2$ is even then we can write $x+2=2k$ for some integer $k$."
You can also just prove this directly if you know that odd integers are of the form $2k+1$. That is, if $x=2k+1$, then $x+2=2(k+1)+1$.
