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in Linear Inequations by (24.8k points)
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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]

1 Answer

+1 vote
by (27.0k points)
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Best 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, ∞)

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