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

1.	Write the solution set of the inequation \|\(\frac{1}{x}\) - 2\| < 4.\|1/x - 2\| < 4
Answer» \|1/x - 2\| < 4 - 4 < (\(\frac{1}{x}\) - 2) < 4 - 2 < \(\frac{1}{x}\) < 6 Part I : \(\frac{1}{x}\) > - 2 ⇒ x < \(\frac{-1}{2}\) Part II : \(\frac{1}{x}\) < 6 ⇒ x > \(\frac{1}{6}\) We have to take union of x < \(\frac{-1}{2}\) and x > \(\frac{1}{6}\) So, the final answer is x ∈ (- ∞,\(\frac{-1}{2}\)) ∪ (\(\frac{1}{6}\),∞).

Write the solution set of the inequation |\(\frac{1}{x}\) - 2| < 4.|1/x - 2| < 4

Answer»

|1/x - 2| < 4

- 4 < (\(\frac{1}{x}\) - 2) < 4

- 2 < \(\frac{1}{x}\) < 6

Part I : \(\frac{1}{x}\) > - 2

⇒ x < \(\frac{-1}{2}\)

Part II : \(\frac{1}{x}\) < 6

⇒ x > \(\frac{1}{6}\)

We have to take union of x < \(\frac{-1}{2}\) and x > \(\frac{1}{6}\)

So, the final answer is x ∈ (- ∞,\(\frac{-1}{2}\)) ∪ (\(\frac{1}{6}\),∞).