Solve for x, the inequalities Exercises. 1 |x|-3 1 2 - Vidyadip

Question

Solve for x, the inequalities Exercises.
$\frac{1}{|\text{x}|-3}\leq\frac{1}{2}$

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Answer

Given that $\frac{1}{|\text{x}|-3}\leq\frac{1}{2}$
$\Rightarrow|\text{x}|-3\geq2$
$\Rightarrow|\text{x}|\geq5$
So, $\text{x}\in(-\infty, -5)\cup(5, \infty)\ ...(\text{i})$
Here $|\text{x}|-3\neq0$
$|\text{x}|-3<0$ or $|\text{x}|-3>0$
$|\text{x}|<3$ or $|\text{x}|>3$
$-3<\text{x}<3, \text{x}<-3, \text{x}>3\ ...(\text{ii})$
From in eq. (i) and (ii) we get
$\text{x}\in(-\infty, -5)\cup(-3, 3)\cup(5, \infty)$

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