Write the solution set of the inequation |1/x - 2| < 4 ​

Question

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

|1/x - 2| < 4

Answer 1

|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 ∈ (- ∞,\(\frac{-1}{2}\)) ∪ (\(\frac{1}{6}\),∞).