If |x-2| ≤ 1 , then

Correct answer: (A) x ∈[1,3]. Given that, |x-2| ≤ 1 We know that, |x| ≤ a ⇒-a ≤ x ≤ a So, -1 ≤ x-2 ≤ 1 ⇒ 1 ≤ x ≤ 3 Therefore x ∈[1,3]

Q65 / 180 · KCET 2017 · Mathematics

If $ |x-2| \leq 1 $, then

Correct answer
A
$ \mathrm{x} \in[1,3] $
B
$ \mathrm{x} \in(1,3) $
C
$ x \in[-1,3) $
D
$ x \in(-1,3) $

Solution

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 $x \in[1,3]$

Hence, the correct answer is option: 'A'.

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

Solution

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