If A = {x ∈ R : 2x − 1 ≥ 5}, what is the interval form of A?
Answer and explanation
Correct answer: [3, ∞)
Solve the defining inequality step by step: 2x − 1 ≥ 5. Adding 1 to both sides gives 2x ≥ 6, and dividing by the positive number 2 gives x ≥ 3. Thus A contains 3 and every real number greater than 3. In interval notation, inclusion of 3 is shown by a square bracket, while infinity always uses a parenthesis. Therefore A = [3,∞), so B is correct.
Frequently asked questions
What is the correct answer to this question?
[3, ∞)
Why is this the correct answer?
Solve the defining inequality step by step: 2x − 1 ≥ 5. Adding 1 to both sides gives 2x ≥ 6, and dividing by the positive number 2 gives x ≥ 3. Thus A contains 3 and every real number greater than 3. In interval notation, inclusion of 3 is shown by a square bracket, while infinity always uses a parenthesis. Therefore A = [3,∞), so B is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
