Division Algorithm

[Trumbone]

I am struggling to prove that 10q+r is divisible by 7 iff q-2r is divisble by 7 where q and r are natural numbers.
Does anyone have any tips of how to start either direction of the proof? Thank you.

 

[Deleted member 4993]

I am struggling to prove that 10q+r is divisible by 7 iff q-2r is divisble by 7 where q and r are natural numbers.
Does anyone have any tips of how to start either direction of the proof? Thank you.

Hint:

21r is always divisible by 7 and according to assumption so is 10(q-2r).