Question:
For how many integers n, will the inequality \((n – 5) (n – 10) – 3(n – 2) ≤ 0\) be satisfied?
For how many integers n, will the inequality \((n – 5) (n – 10) – 3(n – 2) ≤ 0\) be satisfied?
Updated On: Sep 26, 2024
- 11
- 14
- 21
- 13
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The Correct Option is A
Solution and Explanation
The inequality \((n−5)(n−10)−3(n−2)≤0\) can be expressed as \(n^2−18n+56≤0\), further simplified to \((n−4)(n−14)≤0. \)
Since n is an integer, it can take values from 4 to 14 (inclusive), resulting in a total of 11 possible values.
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