SOLUTION: Hi need some help with solving this problem. Solve, (x+11)(x-9)(x+3)>0 the solution set is {x|____}. Thank you :o)

Algebra ->  Test -> SOLUTION: Hi need some help with solving this problem. Solve, (x+11)(x-9)(x+3)>0 the solution set is {x|____}. Thank you :o)      Log On


   

Question 356179: Hi need some help with solving this problem.
Solve,
(x+11)(x-9)(x+3)>0 the solution set is {x|____}.
Thank you :o)
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,-11)
Region 2:(-11,-3)
Region 3:(-3,9)
Region 4:(9,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:Choose x=-12
%28x%2B11%29%28x-9%29%28x%2B3%29%3E0+
%28-12%2B11%29%28-12-9%29%28-12%2B3%29%3E0+
%28-1%29%28-21%29%28-9%29%3E0+
-189%3E0+
False, Region 1 is not part of the solution region.
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Region 2:Choose x=-4
%28x%2B11%29%28x-9%29%28x%2B3%29%3E0+
%28-4%2B11%29%28-4-9%29%28-4%2B3%29%3E0+
%287%29%28-13%29%28-1%29%3E0+
91%3E0+
True, Region 2 is part of the solution region.
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Region 3:Choose x=0
%28x%2B11%29%28x-9%29%28x%2B3%29%3E0+
%280%2B11%29%280-9%29%280%2B3%29%3E0+
%2811%29%28-9%29%283%29%3E0+
-297%3E0+
False, Region 3 is not part of the solution region.
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Region 4:Choose x=10
%28x%2B11%29%28x-9%29%28x%2B3%29%3E0+
%2810%2B11%29%2810-9%29%2810%2B3%29%3E0+
%2821%29%281%29%2813%29%3E0+
91%3E0+
True, Region 4 is part of the solution region.
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Solution Region: (-11,-3) U (9,infinity)
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Graphical verification: Look for regions where the function is above the x-axis (y%3E0)
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