If c divides a, then prove cx divides ax.

Question

I have a = ck for some integer k and ax = cxj for some integer j. I am not really sure where to go from here. If I put a into the second equation it would become ckx = cxj, and so the implication would only be true when k = j.

Answer 1

$$c\mid a\implies a= mc . \text{ And now multiply both sides by}\;\;x\ldots$$