Question 92216: Find the solution sets for the following:
3x^2-2x-8/x-1 >= 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the solution sets for the following:
3x^2-2x-8/x-1 >= 0
Factor:
[(x-2)(3x+4)]/[x-1] >=0
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Zeroes are x=2 and x=-4/3
The domain excludes x=1
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Draw a number line and plot the values x=-4/3, x=1, x=2
Pick a test point from each interval of the number line bordered
by these values of x.
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If x=-10 you get (-12*-26)/-11>=0; this is false; no solution in (-inf,-4/3)
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If x=0 you get (-2*4/-1)>=0; this is true; solutions in [-4/3,1)
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If x=3/2 you get ((-1/2) * (17/2)/(1/2))>=0; false so no solution in (1,2)
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If x=3 you get (8*13/2)>=0 ; true so solutions in [2,inf)
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Final Solution:
[-4/3,1) U [2,inf)
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Cheers,
Stan H.
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