If |x + 2| ≤ 9, then ______. - Mathematics

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MCQ
Fill in the Blanks

If |x + 2| ≤ 9, then ______.

Options

  • x ∈ (–7, 11)

  • x ∈ [–11, 7]

  • x ∈ (–∞, –7) ∪ (11, ∞)

  • x ∈ (–∞, –7) ∪ [11, ∞)

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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]

Concept: Inequalities - Introduction
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APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 6 Linear Inequalities
Exercise | Q 25 | Page 109
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