Question 90877
x/(x-3) <= -8/(x-6)
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1st: Find values x cannot take:
x=3 and x=6
2nd: Plot those on a number line:
Comment: That breakes the number line into 3 intervals.
Check each interval with a test value to see where the 
solution set is.
3rd: Test point check.
Interval (-inf,-3)
Test Point x=-10
Substitute in the original inequality:
-10/(-13)<=-8/-16; 10/13 <= 1/2 ; False ; therefore no solutions in (-inf,-3)
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Interval (-3,6)
Test Point x=0
Substitute in the original inequality x/(x-3) <= -8/(x-6):
0 <= -8/-6; 0<=4/3; True ; therefore interval (-3,6) is part of the solution
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Inerval (6,+inf)
Test Point x=10
Substitute in the original inequality:
10/7 <=-8/4 10/7 <- -2; False; therefore no solutions in (6,+inf)
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Final Answer: -3 < x < 6 is the solution set.
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Cheers,
Stan H.