Question

If $\left|\frac{2}{x-5}\right|>1,$ then $x$ belongs to the interval

• A. $(3,7)$
• B. $(3,5)\cup (5,7)$
• C. $[3,7]-\left\{5\right\}$
• D. $R-\left\{5\right\}$

Answer 1

The correct option is B $(3,5)\cup (5,7)$

$\frac{2}{|x-5|}>1$
$\Rightarrow |x-5|<2,x\ne 5$
$\Rightarrow -2<x-5<2,x\ne 5$
$\Rightarrow 3<x<7$
$\therefore x\in (3,5)\cup (5,7)$