Divisibility of Integers and TD

Question

Is it true that if $3|x$ and $3|y$ and $3|z$ then $3|(x+y+z)?$
If yes how do I prove it?
If not how do I work through a problem like this?

Answer 1

$3a=x,\ 3b=y,\ 3c=z,$ now factor out $3$ and put $d=a+b+c.$ Then $3d=x+y+z$ so...