SOLUTION: Find and graph the solution set: x^3 - 16x > 0

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Question 318840: Find and graph the solution set: x^3 - 16x > 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3+-+16x+%3E+0
x%28x%5E2-16%29%3E0
x%28x-4%29%28x%2B4%29%3E0
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Break up the number line into four parts.
Region 1: (-infinity,-4)
Region 2: (-4,0)
Region 3: (0,4)
Region 4: (4,infinity)
Pick a point in each region (not at the endpoints) and test the function.
If it solves the equation, it's in the solution region.
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Region 1: x=-5
x%28x-4%29%28x%2B4%29%3E0
-5%28-5-4%29%28-5%2B4%29%3E0
-5%28-9%29%28-1%29%3E0
-45%3E0
False, Region 1 is not part of the solution.
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Region 2: x=-2
x%28x-4%29%28x%2B4%29%3E0
-2%28-2-4%29%28-2%2B4%29%3E0
-2%28-6%29%282%29%3E0
24%3E0
True, Region 2 is part of the solution.
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Region 3: x=2
x%28x-4%29%28x%2B4%29%3E0
2%282-4%29%282%2B4%29%3E0
2%28-2%29%286%29%3E0
-24%3E0
False, Region 3 is not part of the solution.
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Region 4: x=5
x%28x-4%29%28x%2B4%29%3E0
5%285-4%29%285%2B4%29%3E0
5%281%29%289%29%3E0
45%3E0
True, Region 4 is part of the solution.
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Solution:(-4,0) U (4,infinity)
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Graphical verification of the results.
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