Question

Solve the following inequality:
${\left(\frac{1}{5}\right)}^{\frac{2x+1}{1-x}}>{\left(\frac{1}{5}\right)}^{-3}$

Answer 1

${\left(\frac{1}{5}\right)}^{\frac{2x+1}{1-x}}>{\left(\frac{1}{5}\right)}^{-3}$

$(5{)}^{\frac{2x+1}{x-1}}>5^3$

$\frac{2x+1}{x-1}>3$

$\frac{2x+1-3(x-1)}{x-1}>0$

$\frac{2x+1-3x+3}{x-1}>0$

$\frac{4-x}{x-1}>0$

$\frac{x-4}{x-1}<0$

$x\epsilon (1,4)$