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Answer:
(-∞ < x < 0) ∪ (0 < x < 8)
Step-by-step explanation:
Factoring the inequality gives you ...
x²(x -8) < 0
The x-intercepts of the curve described by the left-side expression are 0 and 8, values that make the factors zero. The intercept at x=0 has multiplicity 2, so the curve does not cross the x-axis there.
Since this is an odd-degree polynomial with a positive leading coefficient, its general shape is rising to the right. That means the left-side expression will be negative for x-values less than the first x-intercept, and for x-values between the x-intercepts.
The solution is ...
(-∞ < x < 0) ∪ (0 < x < 8)
