Question

plz reply this question fast​ and plz give its step by step solution..

Answer 1

We're given,

$\dfrac{1}{|x|-3}\leq\dfrac{1}{2}$

On taking the reciprocal of both, we get,

$|x|-3\geq 2$

Adding 3 to both sides,

$|x|\geq 5$

This holds true if x is a positive number greater than or equal to 5 and x is a negative number less than or equal to -5, since $|5|=|-5|=5.$

I.e., $x\geq 5\ \ \&\ \ x\leq -5$

Hence the answer in interval notation is,

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

We can say this is the domain of the equation.