Hi,

Could anyone help me solve the following inequalities algebraically?

2^x-3<x+1

(x+1)(x-2)(2^x)>0

My teacher mentioned something about Newton's method for solving the first one, but he wouldn't explain it to us. I did some research, but I still don't really understand, other than that I have to estimate a zero of 2^x-x-4>0 and use tangents to find a very close approximation of the actual root. As for the second, I can come up with the answer through reasoning and logic, but I would like to know how to solve it algebraically.

Thanks in advance! =]