SOLUTION: 3x-1/x-7 is less than or equal to 4 inequality problem using infinity

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Question 353487: 3x-1/x-7 is less than or equal to 4 inequality problem using infinity
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%283x-1%29%2F%28x-7%29%3C=4
%283x-1%29%2F%28x-7%29-4%3C=0
%283x-1%29%2F%28x-7%29-%284%28x-7%29%29%2F%28x-7%29%3C=0
%283x-1-4%28x-7%29%29%2F%28x-7%29%3C=0
%283x-1-4x%2B28%29%2F%28x-7%29%3C=0
%2827-x%29%2F%28x-7%29%3C=0
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Break up the number line into 3 regions using the critical points from the equation.
Region 1:(-infinity,7)
Region 2:(7,27)
Region 3:(27,infinity)
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For each region pick a test point (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution region.
Region 1:x=0
%2827-x%29%2F%28x-7%29%3C=0
%2827%29%2F%28-7%29%3C=0
-27%2F7%3C=0
True, this region is part of the solution.
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Region 2:x=10
%2827-10%29%2F%2810-7%29%3C=0
17%2F3%3C=0
False, this region is not part of the solution.
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Region 1:x=30
%2827-30%29%2F%2830-7%29%3C=0
-3%2F23%3C=0
True, this region is part of the solution.
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Solution region: (-infinity,7) U (27,infinity)