Find the solution set of the in equation \(\frac{1}{{\text{x}} - 2}<0

1.	Find the solution set of the in equation \(\frac{1}{{\text{x}} - 2}<0\)
Answer» \(\frac{1}{{\text{x}} - 2}<0\) 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)

Find the solution set of the in equation \(\frac{1}{{\text{x}} - 2}<0\)

Answer»

\(\frac{1}{{\text{x}} - 2}<0\)

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)