Question

If |x + 2| ≤ 9, then ______.

विकल्प

• x ∈ (–7, 11)

• x ∈ [–11, 7]

• x ∈ (–∞, –7) ∪ (11, ∞)

• x ∈ (–∞, –7) ∪ [11, ∞)

Answer 1

If |x + 2| ≤ 9, then x ∈ [– 11, 7].

Explanation:

Given that |x + 2| ≤ 9

⇒ –9 ≤ x + 2 ≤ 9

⇒ –9 – 2 ≤ x ≤ 9 – 2  ......[|x| < a ⇒ –a ≤ x ≤ a]

⇒ –11 ≤ x ≤ 7

⇒ x ∈ [–11, 7]