SOLUTION: how do I solve h(x)=5x/(x-8)(x+3)>=0

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Question 322251: how do I solve h(x)=5x/(x-8)(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.
Region 1:(-infinity,-3)
Region 2:(-3,0]
Region 3:[0,8)
Region 4:(8,infinity)
The regions cannot contain x=-3 and x=8 since there is a discontinuity at those points.
Hence the use of "(" and ")" instead of "[" and "]" at those points.
Choose a point in each region (not an endpoint) and test the inequality.
If the point satisfies the inequality, the region is part of the solution region.
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Region 1: Let x=-5
5x%2F%28%28x-8%29%28x%2B3%29%29%3E=0
-25%2F%28%28-13%29%28-2%29%29%3E=0
-25%2F26%3E=0
False, Region 1 is not in the solution region.
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Region 2: Let x=-2
5x%2F%28%28x-8%29%28x%2B3%29%29%3E=0
-10%2F%28%28-10%29%281%29%29%3E=0
1%3E=0
True, Region 2 is part of the solution region.
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Region 3: Let x=5
5x%2F%28%28x-8%29%28x%2B3%29%29%3E=0
25%2F%28%28-3%29%288%29%29%3E=0
-25%2F24%3E=0
False, Region 3 is not part of the solution region.
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Region 4: Let x=10
5x%2F%28%28x-8%29%28x%2B3%29%29%3E=0
50%2F%28%282%29%2813%29%29%3E=0
50%2F26%3E=0
True, Region 4 is part of the solution region.
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Solution Region:(-3,0] U (8,infinity)
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Graphical verification with h(x) plotted.
Look for regions where h%28x%29%3E=0
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