Question

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

• A. $-3$
• B. $-5$
• C. $-4$
• D. $-6$

Answer 1

Answer: (D)

$-6$

$\frac{x-5}{x^2+5x-14}>0$
$\Rightarrow \frac{(x-5)}{(x+7)(x-2)}>0$
$\Rightarrow x-5<0$ and $(x+7)(x-2)<0$
$\Rightarrow x<5$ and $x\in (-7,2)$
So, the smallest integer is $-6$.