How many integers $n$ satisfy $(n - 3)(n - 6) - 3(n - 3) \le 0$?
Answer and solution
Correct answer: 7
Solution
$(n - 3)\big[(n - 6) - 3\big] = (n - 3)(n - 9) \le 0$
$\Rightarrow 3 \le n \le 9$
Integers: $3, 4, 5, 6, 7, 8, 9$ → $7$
$\Rightarrow 3 \le n \le 9$
Integers: $3, 4, 5, 6, 7, 8, 9$ → $7$