What is the set A = {x ∈ ℤ : |x + 2| < 1} equal to?
Answer and explanation
Correct answer: {−2}
Use the standard absolute-value inequality: |x + 2| < 1 is equivalent to −1 < x + 2 < 1. Subtracting 2 throughout gives −3 < x < −1. Among integers, the only number strictly between −3 and −1 is −2. The endpoints −3 and −1 are excluded because the inequality is strict. Thus A contains exactly one element and A = {−2}.
Frequently asked questions
What is the correct answer to this question?
{−2}
Why is this the correct answer?
Use the standard absolute-value inequality: |x + 2| < 1 is equivalent to −1 < x + 2 < 1. Subtracting 2 throughout gives −3 < x < −1. Among integers, the only number strictly between −3 and −1 is −2. The endpoints −3 and −1 are excluded because the inequality is strict. Thus A contains exactly one element and A = {−2}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
