SOLUTION: I need help on solving the inequality *note This is x squared X2+5x<2x+10 x interceps are (-5,0), (2,0)

Algebra ->  Inequalities -> SOLUTION: I need help on solving the inequality *note This is x squared X2+5x<2x+10 x interceps are (-5,0), (2,0)      Log On


   

Question 313395: I need help on solving the inequality
*note This is x squared
X2+5x<2x+10
x interceps are (-5,0), (2,0)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B5x%3C2x%2B10
x%5E2%2B3x-10%3C0
%28x%2B5%29%28x-2%29%3C0
Break up the number line into 3 regions.
Region 1: (-infinity,-5)
Region 2: (-5,2)
Region 3: (2,-infinity)
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Choose a point in each region (not an endpoint) and test the inequality
If it solves the inequality, the region is included in the solution region.
If it doesn't, the region is not included.
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Region 1: x=-6
%28-6%2B5%29%28-6-2%29%3C0
%28-11%29%28-8%29%3C0
88%3C0
False, region 1 is not in the solution region.
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Region 2: x=0
%280%2B5%29%280-2%29%3C0
%285%29%28-2%29%3C0
-10%3C0
True, region 2 is in the solution region.
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Region 3: x=3
%283%2B5%29%283-2%29%3C0
%288%29%281%29%3C0
8%3C0
False, region 3 is not in the solution region.
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Region 2 is the solution region:(-5,2)
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Graphically that is the region when the function drops below the x-axis.
+graph%28+300%2C+300%2C+-8%2C+8%2C+-8%2C+8%2C+%28x%2B5%29%2A%28x-2%29%29+