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Write the set of values of x satisfying |x - 1| ≤ 3 and |x - 1| ≤ 1.

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Write the set of values of x satisfying |x - 1| ≤ 3 and |x - 1| ≤ 1.

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|x – 1| ≤ 3 

⇒ -3 ≤ x – 1 ≤ 3 

⇒ -2 ≤ x ≤ 4 |x – 1 | ≤ 1 

⇒ -1 ≤ x – 1 ≤ 1 

⇒ 0 ≤ x ≤ 2 

We have to take intersection of x ∈ [-2, 4] and x ∈ [0, 2]

So, final answer is x ∈ [0, 2]

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