Question

Solve the following two- sided inequality.
$0<\frac{3x-1}{2x+5}<1$

Answer 1

$\left(i\right)\frac{3x-1}{2x+5}-1<0$

$\frac{3x-1-2x-5}{2x+5}<0$

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

$x\epsilon (\frac{-5}{2},6)-\left(1\right)$

$\left(ii\right)0<\frac{3x-1}{2x+5}$

$\frac{x-\frac{1}{3}}{x+\frac{5}{2}}>0$

$x\epsilon (-\infty ,-\frac{-5}{2})\bigcup (\frac{1}{3},\infty )-\left(2\right)$

$x\epsilon (\frac{1}{3},\infty )-from\left(1\right)\&\left(2\right)$