Question 150464: solve the rational inequality and graph the solution set on a real number line.
x+12
----- < 3
x-9
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! x+12
----- < 3
x-9
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Solve the equality:
x+12 = 3(x-9)
x+12 = 3x-27
2x = 39
x = 19.5
x cannot be 9; x cannot be -12; x cannot be 19.5
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Draw a number line and mark -12 and 9 and 19.5 on it.
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Check a test point in each resulting interval to find the solution set.
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Let x = -13, you get (-13+12)/(-13-9)<3; true so solutions in (-inf,-12)
Let x = 0, you get (0+12)/(0-9) <3; true so solutions in (-12,9)
Let x = 10, you get (10+12)/(10-9)<3 ; false so no solutions in (9,19.5)
Let x = 20, you get (20+12)/(20-9)<3 ; true so solutions in (19.5,+inf)
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Final Answer: (-inf,-12)U(-12,9)U(19.5,+inf)
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Cheers,
Stan H.
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