Question

Solve the following inequality:
${\left(\frac{2}{5}\right)}^{\frac{6-5x}{2+5x}}<\frac{25}{4}$

Answer 1

${\left(\frac{2}{5}\right)}^{\frac{6-5x}{2+5x}}<\frac{25}{4}$

$({\frac{2}{5})}^{\frac{5x-6}{5x+2}}<{\left(\frac{5}{2}\right)}^2$

$\frac{5x-6}{5x+2}<2$

$\frac{5x-6-10x-4}{5x+2}<0$

$\frac{-5x-10}{x+\frac{2}{5}}<0$

$\frac{x+2}{x+\frac{2}{5}}>0$

$x\epsilon (-\infty ,-2)\bigcup (\frac{-2}{5},\infty )$