\(\frac{1}{{\text{x}} - 2}<0\)
We have to find values of x for which \(\frac{1}{{\text{x}} - 2}\) is less than zero that is negative
Now for \(\frac{1}{x - 2}\) to be negative x - 2 should be negative that is x - 2 < 0
⇒ x – 2 < 0
⇒ x < 2
Hence x should be less than 2 for \(\frac{1}{{\text{x}} - 2}<0\)
x < 2 means x can take values from -∞ to 2 hence x ∈ (-∞, 2)
Hence the solution set for \(\frac{1}{{\text{x}} - 2}<0\) is (-∞, 2)