For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?
Explanation:
(n – 5) (n – 10) – 3(n – 2) ≤ 0
⇒ n2 – 15n + 50 - 3n + 6 ≤ 0
⇒ n2 – 18n + 56 ≤ 0
⇒ (n – 4) (n – 14) ≤ 0
As n is an integer, n can be 4, 5, 6 ……14, i.e. it can have 11 values.
Hence, 11.
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