Question

Solution set of the inequality:
${\left(\frac{1}{5}\right)}^{\frac{2x+1}{1-x}}>{\left(\frac{1}{5}\right)}^{-3}$ is

• A. $(-\infty ,-2)\cup (1,\infty )$
• B. $(1,4)$
• C. $(-\infty ,1)\cup (2,\infty )$
• D. none of these

Answer 1

The correct option is B $(1,4)$

${\left(\frac{1}{5}\right)}^{\frac{2x+1}{1-x}}>{\left(\frac{1}{5}\right)}^{-3}$
$\Rightarrow 5^{\frac{2x+1}{x-1}}>5^3$
$\Rightarrow \frac{2x+1}{x-1}>3$
$\Rightarrow \frac{2x+1}{x-1}-3>0$
$\Rightarrow \frac{x-4}{x-1}<0$
Therefore, $x\in (1,4)$
Ans: B