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Question
If |x + 2| ≤ 9, then ______.
Options
x ∈ (–7, 11)
x ∈ [–11, 7]
x ∈ (–∞, –7) ∪ (11, ∞)
x ∈ (–∞, –7) ∪ [11, ∞)
Solution
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]
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