SOLUTION: How do I solve the following inequality using interval notation? 1/x-3 <= 1/x-5

Question 354159: How do I solve the following inequality using interval notation? 1/x-3 <= 1/x-5
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do I solve the following inequality using interval notation?
1/(x-3) <= 1/(x-5)
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x cannot be 3 and it cannot be 5.
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Solve the equality.
1/(x-3) = 1/(x-5)
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x-5 = x-3
No solution: So no solution for the equality part of the problem.
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Draw a number line and plot x = 3 and x = 5.
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Test values in the resulting intervals to find inequality solutions.
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1/(x-3)<1/(x-5)
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If x = 0 you get 1/-3 < 1/-5: true, so solution in (-inf,3)
If x = 4 you get 1/1 < 1/-1: false
If x = 10 you get 1/7 < 1/5: true, so solutions in (5,+inf)
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Cheers,
Stan H.

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