SOLUTION: Ok, I am supposed to solve the follow inequality and then graph it on a number line. Here is the example: (x-5)(x-6)(x-7)greater than or equal to 0. Can you explain in detail how t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Ok, I am supposed to solve the follow inequality and then graph it on a number line. Here is the example: (x-5)(x-6)(x-7)greater than or equal to 0. Can you explain in detail how t      Log On


   

Question 343829: Ok, I am supposed to solve the follow inequality and then graph it on a number line. Here is the example: (x-5)(x-6)(x-7)greater than or equal to 0. Can you explain in detail how to work this?
Thank you,
Suzette Ramos
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Break the number line up into 4 regions.
Region 1: (-infinity,5)
Region 2: (5,6)
Region 3: (6,7)
Region 4: (7,infinity)
Choose a point in each region (not an endpoint).
Test the inequality.
If the inequality is satisfied, that region is part of the solution.
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Region 1:x=0
%28x-5%29%28x-6%29%28x-7%29%3E=0
%28-5%29%28-6%29%28-7%29%3E=0
-210%3E=0
False, this region is not part of the solution region.
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Region 2:x=5.5
%28x-5%29%28x-6%29%28x-7%29%3E=0
%285.5-5%29%285.5-6%29%285.5-7%29%3E=0
0.5%28-0.5%29%28-1.5%29%3E=0
0.375%3E=0
True, this region is part of the solution region.
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Region 3:x=6.5
%28x-5%29%28x-6%29%28x-7%29%3E=0
%286.5-5%29%286.5-6%29%286.5-7%29%3E=0
1.5%280.5%29%28-0.5%29%3E=0
-0.375%3E=0
False, this region is not part of the solution region.
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Region 4:x=10
%28x-5%29%28x-6%29%28x-7%29%3E=0
%2810-5%29%2810-6%29%2810-7%29%3E=0
5%284%29%283%29%3F=0
60%3E=0
True, this region is part of the solution region.
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Solution:(5,6) U (7,infinity)
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You can verify it graphically by plotting the function and checking the regions where the function is greater than zero (above the x-axis).
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