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4.6k views
in Linear Equations by (15.2k points)

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

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1 Answer

+1 vote
by (15.7k points)

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

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)

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