SOLUTION: This is a tough question. Please Help. Solve x/(x � 5)

SOLUTION: This is a tough question. Please Help. Solve x/(x � 5) < 2

Question 87747: This is a tough question. Please Help. Solve x/(x � 5) < 2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve x/(x � 5) < 2
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Rewrite as:
[x/(x-5)] - 2 < 0
Rewrite with a common denominator:
[x/(x-5)] - [2(x-5)/(x-5)] <0
Combine the numerators: to get:
[x-2(x-5)]/(x-5) < 0
[-(x-10)]/[(x-5)] < 0
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The numerator is zero when x=10
The denominator is zero when x=5
Both of these are NOT part of the solution.
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Draw a number line; plot points x=5 and x=10
This breaks the number line into three intervals.
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Determine which interval(s) are part of the solution set:
Pick a sample value from each interval and check it in the INEQUALITY, as follows:
In the interval (-inf,5) pick x=0; then -(0-10)/(0-5)=-2 which is < 0
Therefore all x values in that interval are part of the solution set.
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In the interval (5,10) pick x = 8; then -(8-10)/(8-5)>0
Therefore no values in that interval are part of the solution set.
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In the interval (10,inf) pick x=100; then -(100-10)/(100-5)<0
Therefore all x values in that interval are part of the solution set.
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Conclusion:
The solution is all x-values in (-inf,5) OR (10,inf)
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Cheers,
Stan H.
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