What is the roster form of M = {x : x ∈ ℤ, |x − 2| ≤ 3}?
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Answer and explanation
Correct answer: M = {-1, 0, 1, 2, 3, 4, 5}
For an absolute-value inequality, |x − 2| ≤ 3 means that x is at most 3 units away from 2. Thus, −3 ≤ x − 2 ≤ 3. Adding 2 throughout gives −1 ≤ x ≤ 5. Since x must be an integer, the complete list is −1, 0, 1, 2, 3, 4, and 5. Hence the roster form is option A.
Frequently asked questions
What is the correct answer to this question?
M = {-1, 0, 1, 2, 3, 4, 5}
Why is this the correct answer?
For an absolute-value inequality, |x − 2| ≤ 3 means that x is at most 3 units away from 2. Thus, −3 ≤ x − 2 ≤ 3. Adding 2 throughout gives −1 ≤ x ≤ 5. Since x must be an integer, the complete list is −1, 0, 1, 2, 3, 4, and 5. Hence the roster form is option A.
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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