Question

The largest negative integer for which the inequality $\frac{(x-3)(x-2)}{(x-1)(x-5)}>0$ holds true is

• A. $-2$
• B. $-1$
• C. $-3$
• D. $-4$

Answer 1

The correct option is B $-1$

Inequality $\Rightarrow \frac{(x-3)(x-2)}{(x-1)(x-5)}>0$

Refer above image.

$\Rightarrow$ Inequality is satisfied when

$xϵ(-\infty ,1)\cup (2,3)\cup (5,\infty )$

$\Rightarrow$ Here the largest negative integer is $-1$

in the interval $(-\infty ,1)$.