If E = {x : x ∈ ℤ, |x − 2| ≤ 3}, how many elements are in E?
Answer and explanation
Correct answer: 7
Use the standard absolute-value inequality rule: |x − 2| ≤ 3 is equivalent to −3 ≤ x − 2 ≤ 3. Adding 2 to all parts gives −1 ≤ x ≤ 5. The integers in this closed interval are −1, 0, 1, 2, 3, 4 and 5. Counting them gives 7 elements, so option C is correct. The closed endpoints must be included because the original sign is ≤.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Use the standard absolute-value inequality rule: |x − 2| ≤ 3 is equivalent to −3 ≤ x − 2 ≤ 3. Adding 2 to all parts gives −1 ≤ x ≤ 5. The integers in this closed interval are −1, 0, 1, 2, 3, 4 and 5. Counting them gives 7 elements, so option C is correct. The closed endpoints must be included because the original sign is ≤.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
