Question

The minimum integral value of the x for which $\frac{x-2}{x+5}>2$ is .

• A. -12
• B. -11
• C. -10
• D. -13

Answer 1

The correct option is B -11

$\frac{x-2}{x+5}>2\Rightarrow \frac{x-2}{x+5}-2>0\Rightarrow \frac{x-2-2(x+5)}{x+5}>0\Rightarrow \frac{x-2-2x-10}{x+5}>0\Rightarrow \frac{-(x+12)}{x+5}>0\Rightarrow \frac{x+12}{x+5}<0x+12>0\mathrm{and}x+5<0\Rightarrow x>-12\mathrm{and}x<-5\mathrm{OR}x+12<0\mathrm{and}x+5>0\Rightarrow x<-12\mathrm{and}x>-5\left(\mathrm{This}\mathrm{is}\mathrm{not}\mathrm{possible}\right)\mathrm{Hence},x>-12\mathrm{and}x<-5.\mathrm{Minimum}\mathrm{integral}\mathrm{value}\mathrm{of}x\mathrm{satisfying}\mathrm{the}\mathrm{given}\mathrm{inequality}\mathrm{is}-11.$