Question

If |x − 1| > 5, then ______.

विकल्प

• x ∈ (–4, 6)

• x ∈ [–4, 6]

• x ∈ [–∞, –4) ∪ (6, ∞)

• x ∈ [–∞, –4) ∪ [6, ∞)

Answer 1

If |x −1| > 5, then x ∈ [–∞, – 4) ∪ (6, ∞).

Explanation:

Given that |x − 1| > 5

⇒ (x – 1) < –5 or (x – 1) > 5

⇒ x < –5 + 1 or x > 5 + 1

⇒ x < –4 or x > 6

⇒ x ∈ [–∞, –4) ∪ (6, ∞)