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Question
x and b are real numbers. If b > 0 and |x| > b, then ______.
Options
x ∈ (–b, ∞)
x ∈ [–∞, b)
x ∈ (–b, b)
x ∈ (–∞, –b) ∪ (b, ∞)
Solution
x and b are real numbers. If b > 0 and |x| > b, then x ∈ (–∞, –b) ∪ (b, ∞).
Explanation:
Given that |x| > b, b > 0
⇒ x < –b or x > b
⇒ x ∈ (–∞, –b) ∪ (b, ∞)
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