Question

Solve the following inequality:
$2^x+2^{-x+1}-3<0$

Answer 1

$2^x+2^{-x+1}-3<0$

$2^x+\frac{2}{2^x}-3<0$

$let{2}^x=t(t>0)$

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

$t^2-3t+2<0$

$t^2-2t-t+2<0$

$(t-2)(t-1)<0$

$t\epsilon (1,2)$

$2^x\epsilon (1,2)$

$x\epsilon (0,1)$