If |x - 1| ≤ 2, then x belongs to which interval?

Model Answer & Options

Source: Extra Practice

(-1, 3)

[-1, 3]

[1, 3]

[-3, 1]

Explanation

The absolute value inequality |x - a| ≤ r is equivalent to a - r ≤ x ≤ a + r. Here, a = 1 and r = 2. So, 1 - 2 ≤ x ≤ 1 + 2, which gives -1 ≤ x ≤ 3. In interval notation, this is [-1, 3]. Option 1 is incorrect because it uses open intervals. Options 3 and 4 are incorrect due to calculation errors in applying the boundary values.

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