If $$n$$ is an integer such that $$\frac{|n+6| - |n-3|}{\sqrt{100 - n^3}} \geq 0$$, then the number of possible values of $$n$$ is ____

Correct Answer: 6

Numerator $$|n+6| - |n-3| \geq 0$$ iff $$n \geq -1.5$$, i.e., $$n \geq -1$$ for integers.

Denominator $$\sqrt{100-n^3} > 0$$ requires $$n^3 < 100$$, so $$n \leq 4$$.

Valid integers: $$n \in \{-1, 0, 1, 2, 3, 4\}$$. Count = 6.

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