SOLUTION: x^2+8x+7>0 X^3-x^2-6X>0

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Question 338692: x^2+8x+7>0
X^3-x^2-6X>0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B8x%2B7%3E0
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Break up the number line into 3 regions.
Region 1: (-infinity,-7)
Region 2: (-7,-1)
Region 3: (-1,infinity)
Choose a point in each 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=-8
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%28-7%29%28-1%29%3E0
7%3E0
True, this region is part of the solution.
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Region 2: x=-2
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%28-2%2B1%29%28-2%2B7%29%3E0
%28-1%29%285%29%3E0
-5%3E0
False, this region is not part of the solution.
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Region 3: x=0
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7%3E0
True, this region is part of the solution.
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Solution: (-infinity,-7) U (-1,infinity)
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x%5E3-x%5E2-6x%3E0
x%28x%5E2-x-6%29%3E0
x%28x-3%29%28x%2B2%29%3E0
Break up the number line into 4 regions.
Region 1: (-infinity,-2)
Region 2: (-2,0)
Region 3: (0,3)
Region 4: (3,infinity)
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Follow the same procedure as outlined above to find the solution region.