question_answer

The smallest integer x for which the inequality \[\frac{x-5}{{{x}^{2}}+5x-14}>0\] is satisfied is given by

A) \[-\,6\]  

B) \[-\,5\]

C) \[-\,4\]                          

D) \[-\,3\]

Correct Answer: A

Solution :

\[\frac{(x-5)}{{{x}^{2}}+5x-14}>0\]

\[\frac{(x-5)}{(x+7)\,\,(x-2)}>0\]

\[x\in (-7,\,\,2)\cup (5,\,\,\infty )\]

Smallest integer x is \[-\,6\]