If E = {x : x ∈ Z, −3 ≤ x/2 < 4}, how many elements does E have?
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Answer and explanation
Correct answer: 14
Because 2 is positive, multiplying the compound inequality by 2 preserves both inequality signs: −6 ≤ x < 8. Since x must be an integer, the values are −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, and 7. Counting them gives 8 − (−6) = 14 integers, with the upper endpoint 8 excluded. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Because 2 is positive, multiplying the compound inequality by 2 preserves both inequality signs: −6 ≤ x < 8. Since x must be an integer, the values are −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, and 7. Counting them gives 8 − (−6) = 14 integers, with the upper endpoint 8 excluded. Therefore option A is correct.
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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