Number Theory logica problem

I have a given problem and attempted to solve it. I would like to know if i'm solving it right or not.

For all integers a and b, if a divides b, then a+a divides b+b. True or false

What i think is that if you let a=5 and b=20, then it is true because 5+5 divides 20+20, 10 divides 40 which is 4. however if you let a=5 and b=17, then it is false bc 10 cannot divide 34. well it can, 1.5 but i don't know 1.5 can be included...

any help would be great

Thank you