Question

Write the solution set of the inequation $|\frac{1}{x}-2|<4$

Answer 1

$|\frac{1}{x}-2|>4\iff \frac{1}{x}<2-4or\frac{1}{x}>2+4\iff \frac{1}{x}<-2or\frac{1}{x}>6\iff \frac{-1}{x}>2or\frac{1}{x}>6\iff \frac{-1}{2}>xor\frac{1}{6}>x\iff xϵ(-\infty ,\frac{-1}{2})orxϵ(\frac{1}{6},\infty )\iff xϵ(-\infty ,\frac{-1}{2})\cup (\frac{1}{6},\infty )$

Hence,the solution set of the given system of inequations is $(-\infty ,\frac{-1}{2})\cup (\frac{1}{6},\infty )$