Question 78080: solve the folowing inequation
x+3/x-2 less than equal to 2
i have solved this in the following way
x+3/ x-2 - 2 less than equal to 0
-x+7 / x-2 less than equal to 0
x-7/ x-2 greater than equal to 0
x belongs to (- infinity, 2 ) union [ 7, infinity)
SIR I CANNOT UNDERSTAND THIS FORM
x belongs to (- infinity, 2 ) union [ 7, infinity)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve the folowing inequation
x+3/x-2 <= 2
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1st: Notice that x cannot be 2 because x-2 is in the denominator.
2nd: Solve the equality:
(x+3)/(x-2)=2
x+3 = 2x-4
x=7 (so that is a point in the solution set.
3rd:
Draw a line.
Plot the two values x=2 and x=7 on the line.
This breaks the line into three intervals ; pick a test point in each
interval to see where the solution set(s) lie.
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Interval (-inf,2); pick x=0; substitute into the inequality: 3/-2<2
that is true so the interval is part of the solution set.
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Interval (2,7] ; pick x=5; substitute to get 8/3<2; false; no solutions here
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Interval [7,inf); pick x=10; substitute to get 13/8<2; true; solutions here.
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Final Answer:
x is an element of (-inf,2) OR [7,inf}
Cheers,
Stan H.
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