Question

If $\frac{x-2}{x+5}>2$, then $x\in$

• A. $(-12$, $5)$
• B. $(-12$, $-5)$
• C. $(-5$, $12)$
• D. $(5$, $12)$

Answer 1

Answer: (B)

We have $\frac{x-2}{x+5}>2$
$\Rightarrow \frac{x-2}{x+5}-2>0\Rightarrow \frac{-\left(x+12\right)}{x+5}>0\Rightarrow \frac{x+12}{x+5}<0$
$\Rightarrow x+12>0$ and $x+5<0$
or $x+12<0$ and $x+5>0$
$\Rightarrow x>-12$ and $x<-5$
or $x<-12$ and $x>-5$ (Not possible)
Therefore, $-12<x<-5$, i.e. $x\in$ $(-12$, $-5)$