Proof by Induction (concerning $3^nge1+2n$)

I've been able to follow the idea and steps of induction so far but I've hit a road block in understanding one of the examples in a text book. This is what the book says p.97:

Prove: $3^n \geq1 + 2n$

Skipping past the base case and assuming it's true, the books inductive step is as follows:

Show: $3^{n+1} = 1 + 2(1+n)$

LHS $= 3\cdot 3^n$
LHS $\geq 3(1+2n)$ [by assumption]
LHS $\geq 1+2+2n+4n$ [algebra]
LHS $\geq 1+2(1+n)$ [since $n>0$]

How can the $4n$ be omitted by $n>0$?
This really boggles me, appreciate any insights and help.

Thanks!

Answer

If n>0 then 4n>0 and omitting it from the RHS reduces the value. So >= still applies - or applies more strongly, and the = could be dropped.