Prove Bernoulli's inequality via induction

(1 + x)n ≥ 1 + nx

I can work it down to this step but I have no idea where to go from here to finish the equation.

(1 + x)^k (1 + x) ≥ 1 + x + kx + kx2

Looking at the inductive step (you're very close):
(1 + x)^(k+1)
= (1 + x)^k (1 + x)
≥ (1 + kx) (1 + x), by inductive hypothesis
= 1 + (k+1) x + x^2
≥ 1 + (k+1) x + 0
= 1 + (k+1) x.

I hope this helps!