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