SOLUTION: 5.how do I solve the inequality and give the answer in interval notation? (x+8)(x+3)(x-3)>0 ?????

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Question 364997: 5.how do I solve the inequality and give the answer in interval notation?
(x+8)(x+3)(x-3)>0 ?????

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Break up the number line into 4 regions using the critical points of the function.
Region 1:(-infinity,-8)
Region 2:(-8,-3)
Region 3:(-3,3)
Region 4:(3,infinity)
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For each region, choose a point in the region (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution region.
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Region 1:x=-9
%28x%2B8%29%28x%2B3%29%28x-3%29%3E0
%28-9%2B8%29%28-9%2B3%29%28-9-3%29%3E0
%28-1%29%28-6%29%28-12%29%3E0+
-72%3E0+
False, Region 1 is not part of the solution region.
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Region 2x=-4%7D%7D%0D%0A%7B%7B%7B%28x%2B8%29%28x%2B3%29%28x-3%29+%3E0
%28-4%2B8%29%28-4%2B3%29%28-4-3%29%3E0
%284%29%28-1%29%28-7%29%3E0+
28%3E0+
True, Region 2 is part of the solution region.
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Region 3:x=0
%28x%2B8%29%28x%2B3%29%28x-3%29%3E0
%288%29%283%29%28-3%29%3E0
-72%3E0+
False, Region 4 is not part of the solution region.
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Region 4:x=4
%28x%2B8%29%28x%2B3%29%28x-3%29%3E0
%284%2B8%29%284%2B3%29%284-3%29%3E0
%2812%29%287%29%281%29%3E0+
84%3E0+
True, Region 4 is part of the solution region.
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Solution Region:(-8,-3) U (3,infinity)
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Graphical verification: Look for regions where the function is above the x-axis (y%3E0)
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