"Solve the equation: 16^n < 8^n+1"

So far, I got this:

(2^4)^n < (2^3)^n+1 --------- rewrote with a base of two

4n < 3(n+1) ------------------ property of equality for exponential functions

4n < 3n+3 ---------- as far as I could get

The solution in the text is n < 3, but I don't understand how this could be? I've tried dividing the left and right side by 4, but that would cause me to end up in error with n > 3/4n+3/4.

Thanks in advance.