Question

Solve the following inequality:
$\frac{2^{x-1}-1}{2^{x+1}+1}<2$

Answer 1

$\frac{2^{x-1}-1}{2^{x+1}+1}<2$

$\frac{2^{x-1}-1-2(2^{x+1}+1)}{2^{x+1}+1}<0$

$2^{x+1}+1>0$

$\frac{2^x}{2}-1-2(2.2^x+1)<0$

$\frac{2^x}{2}-1-4.2^x-2<0$

$let{2}^x=t$

$\frac{t}{2}-1-4t-2<0$

$\frac{t}{2}-4t-3<0$

$t-8t-6<0$

$-7t<6$

$t>\frac{-6}{7}$

$butt=2^x>0$

$xisallrealnumbers$