SOLUTION: write x square plus eight x minus twenty is less tha zero in interval notation form

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Question 367675: write x square plus eight x minus twenty is less tha zero in interval notation form




Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B8x-20%3C0
%28x%2B10%29%28x-2%29%3C0
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Break up the number line into 3 regions using the critical points of the function.
Region 1:(-infinity,-10)
Region 2:(-10,2)
Region 3:(2,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=-11
%28x%2B10%29%28x-2%29%3C0
%28-11%2B10%29%28-11-2%29%3C0
%28-1%29%28-13%29%3C0+
13%3C0+
False, Region 1 is not part of the solution region.
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Region 2:x=0
%28x%2B10%29%28x-2%29%3C0
%2810%29%28-2%29%3C0
-20%3C0+
True, Region 2 is part of the solution region.
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Region 3:x=3
%28x%2B10%29%28x-2%29%3C0
%283%2B10%29%283-2%29%3C0
%2813%29%281%29%3C0+
13%3C0+
False, Region 3 is not part of the solution region.
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Solution Region:(-10,2)
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Graphical verification: Look for regions where the function is below the x-axis (y%3C0)
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