Question

Identify the solution set for $\frac{1}{\left|x\right|-3}<\frac{1}{2}$

• A. (-3,2)
• B. $(-\infty ,-5)\cup (5,\infty )$
• C. $(5,\infty )$
• D. $(-\infty ,-5)\cup (-3,3)\cup (5,\infty )$

Answer 1

The correct option is B $(-\infty ,-5)\cup (5,\infty )$

$\frac{1}{\left|x\right|-3}<\frac{1}{2}$
Solution:
Since, $\frac{1}{\left|x\right|-3}<\frac{1}{2}$
$\therefore |x|-3>2$
$\therefore |x|>5$
$\therefore x<-5$ and $x>5$
Hence, solution set for $\frac{1}{\left|x\right|-3}<\frac{1}{2}$ is $(-\infty ,-5)\cup (5,\infty )$