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Find the solution set of the in equation \(\frac{|{\text{x}}-2|}{({\text{x}}-2)}\) < 0. x ≠ 2 |
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Answer» \(\frac{|{\text{x}}-2|}{({\text{x}}-2)}\) < 0 means we have to find values of x for which \(\frac{|{\text{x}}-2|}{({\text{x}}-2)}\) is negative Observe that the numerator |x – 2| is always positive because of mod, hence for \(\frac{|{\text{x}}-2|}{({\text{x}}-2)}\) to be a negative quantity the denominator (x - 2) has to be negative That is x - 2 should be less than 0 ⇒ x – 2 < 0 ⇒ x < 2 Hence x should be less than 2 for\(\frac{|{\text{x}}-2|}{({\text{x}}-2)}\) < 0 x < 2 means x can take values from -∞ to 2 hence x ∈ (-∞, 2) Hence the solution set for \(\frac{|{\text{x}}-2|}{({\text{x}}-2)}\) < 0 is (-∞, 2) |
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