For how many integers n, will the inequality $(n - 5) (n - 10) - 3(n

Question 26:
For how many integers n, will the inequality $(n - 5) (n - 10) - 3(n - 2)\leq0$ be satisfied?

Answer: 11
Explanation:

$(n - 5) (n - 10) - 3(n - 2)\leq0$
=> $ n^2 - 15n + 50 - 3n + 6 \leq 0$
=> $n^2 - 18n + 56 \leq 0$
=> $(n - 4)(n - 14) \leq 0$
=> Thus, n can take values from 4 to 14. Hence, the required number of values are 14 - 4 + 1 = 11.