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KCET · Maths · Linear Programming

If \( |x-2| \leq 1 \), then

  1. A \( \mathrm{x} \in[1,3] \)
  2. B \( \mathrm{x} \in(1,3) \)
  3. C \( x \in[-1,3) \)
  4. D \( x \in(-1,3) \)
Verified Solution

Answer & Solution

Correct Answer

(A) \( \mathrm{x} \in[1,3] \)

Step-by-step Solution

Detailed explanation

Given that, \(|x-2| \leq 1\)
We know that, \(|x| \leq a \Rightarrow-a \leq x \leq a\)
So, \(-1 \leq x-2 \leq 1\)
\(\Rightarrow 1 \leq x \leq 3\)
Therefore \(x \in[1,3]\)