If A = {x ∈ ℤ : |x + 2| ≤ 1}, which list is correct?
Answer and explanation
Correct answer: A = {−3, −2, −1}
Use the standard absolute-value inequality rule: |x + 2| ≤ 1 is equivalent to −1 ≤ x + 2 ≤ 1. Subtracting 2 throughout gives −3 ≤ x ≤ −1. The integers in this closed interval are −3, −2, and −1. Therefore, A = {−3, −2, −1}. The endpoints are included because the original inequality uses ≤.
Frequently asked questions
What is the correct answer to this question?
A = {−3, −2, −1}
Why is this the correct answer?
Use the standard absolute-value inequality rule: |x + 2| ≤ 1 is equivalent to −1 ≤ x + 2 ≤ 1. Subtracting 2 throughout gives −3 ≤ x ≤ −1. The integers in this closed interval are −3, −2, and −1. Therefore, A = {−3, −2, −1}. The endpoints are included because the original inequality uses ≤.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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