analysis question

How do you show that (1-x)^n>=1-nx for n a natural number and x a real number? 

OP here.  Check out Theorem 1 here:

http://planetmath.org/encyclopedia/11nnIsAnIncreasingSequence.html

I need to show what this theorem is proving, but I don't know about the "Since (1-x)^n>=1-nx, we have" part.  They do not show it, so to me, the proof is somewhat lacking. 

Here, they use substitute n-1 in for x, where n-1>=0 for n=1,2,...