If U = ℝ and A = {x : |x + 2| ≤ 6}, what is A′?
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Answer and explanation
Correct answer: (-∞, -8) ∪ (4, ∞)
Solve the absolute-value inequality: |x + 2| ≤ 6 means −6 ≤ x + 2 ≤ 6. Subtracting 2 gives −8 ≤ x ≤ 4, so A = [−8, 4]. Because the universal set is ℝ, its complement contains numbers strictly less than −8 or strictly greater than 4. Hence A′ = (−∞, −8) ∪ (4, ∞), option A.
Frequently asked questions
What is the correct answer to this question?
(-∞, -8) ∪ (4, ∞)
Why is this the correct answer?
Solve the absolute-value inequality: |x + 2| ≤ 6 means −6 ≤ x + 2 ≤ 6. Subtracting 2 gives −8 ≤ x ≤ 4, so A = [−8, 4]. Because the universal set is ℝ, its complement contains numbers strictly less than −8 or strictly greater than 4. Hence A′ = (−∞, −8) ∪ (4, ∞), option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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