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If \( |x-2| \leq 1 \), then
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Verified Answer
The correct answer is:
\( \mathrm{x} \in[1,3] \)
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 $x \in[1,3]$
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 $x \in[1,3]$
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