If \(\frac{|x-2|}{x-2}\) ≥ 0,then|x-2|/(x-2) ≥ 0,A. x ∈ [2, �

1.	If \(\frac{\|x-2\|}{x-2}\) ≥ 0,then\|x-2\|/(x-2) ≥ 0,A. x ∈ [2, ∞) B. x ∈ (2, ∞) C. x ∈ (−8, 2) D. x ∈ (−∞, 2]
Answer» Option : (B) \|x-2\|/(x-2) ≥ 0 Case I : x > 2 \(\frac{x-2}{x-2}\) ≥ 0 1 ≥ 0 It is true that 1 is always greater than 0 so case I is also true x > 2 Case II : x < 2 \(\frac{-(x-2)}{x-2}\) ≥ 0 -1 ≥ 0 It is false that -1 is not greater than 0 so case II is also false. So, the final solution is x > 2 i.e., x ∈ (2, ∞)

If \(\frac{|x-2|}{x-2}\) ≥ 0,then|x-2|/(x-2) ≥ 0,A. x ∈ [2, ∞) B. x ∈ (2, ∞) C. x ∈ (−8, 2) D. x ∈ (−∞, 2]

Answer»

Option : (B)

|x-2|/(x-2) ≥ 0

Case I : x > 2

\(\frac{x-2}{x-2}\) ≥ 0

1 ≥ 0

It is true that 1 is always greater than 0 so case I is also true x > 2

Case II : x < 2

\(\frac{-(x-2)}{x-2}\) ≥ 0

-1 ≥ 0 It is false that -1 is not greater than 0 so case II is also false.

So, the final solution is x > 2

i.e., x ∈ (2, ∞)