Correct option is A
Given:
Solution:
The expression will be negative,
Since the numerator is positive (1 > 0)
When the denominator (x - 2) is negative, the numerator is always positive (1).
The denominator is negative when x - 2 < 0, or equivalently, x < 2.
However, we must exclude x=2 because the denominator would be zero, which is undefined.
The solution to the inequality is x ∈ (−∞,2).
Lets check by options;
Option (a): xϵ(−∞,2)
This matches our solution.
Option (b): xϵ(−∞,−2)
This means x<−2, which is not the solution.
Option (c): xϵ(2,∞)
This means x>2, which would make the fraction positive.
Option (d): xϵ(−2,∞)
This means x>−2, which includes values greater than 2, making the fraction positive.
Thus, the correct answer is (a).
English
25 Questions
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