I don't think that induction is needed for this problem. I would prove it as follows:

Suppose that x is in N, and that k is a number satisfying 2<=k<=x.

Then, x+k<=x+x=2x<=kx as required.

The first inequatlity follows from the fact that k<=x and the last inequality follows from the fact that 2<=k.

Hope this helps!

Optikal