Which is the correct roster form of L = {x : x ∈ ℤ, |x + 1| < 3}?
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Answer and explanation
Correct answer: L = {−3, −2, −1, 0, 1}
The condition |x + 1| < 3 is equivalent to −3 < x + 1 < 3. Subtracting 1 throughout gives −4 < x < 2. Since x must be an integer, the possible values strictly between −4 and 2 are −3, −2, −1, 0, and 1. The endpoints −4 and 2 are excluded because the inequality is strict, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
L = {−3, −2, −1, 0, 1}
Why is this the correct answer?
The condition |x + 1| < 3 is equivalent to −3 < x + 1 < 3. Subtracting 1 throughout gives −4 < x < 2. Since x must be an integer, the possible values strictly between −4 and 2 are −3, −2, −1, 0, and 1. The endpoints −4 and 2 are excluded because the inequality is strict, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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