Question 109120: I need help solving rational inequalities. I have to solve 4x/x+1 < -3x/x-6 algebraically using a number line and test points. I have to determine when f(x)=4x/x+1 is less than g(x)= -3x/x-6.
I have tried to answer the question but my answer doesn't make any sense to me because I can't tell when f(x) is less than g(x) from when I solved the inequalitie algebraically using the method my teacher taught me.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve 4x/x+1 < -3x/x-6 algebraically using a number line and test points.
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1st: Determine the values x cannot take.
x=0 because the two fractions would be equal
x=-1 and x=6 because the denominators cannot be zero.
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2nd: Draw a number line and mark x=-1, x=0, and x=6
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3rd: Pick a test point from each of the four intervals defined by these x values. Substitute the test value in 4x/x+1 < -3x/x-6 to see if it is true
or false.
In (-inf,-1), pick x=-2, (4*-2)/(-2+1)<(-3*-2)/(-2-6) , false
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In (-1,0), pick x=-1/2, (-2)/(1/2))<(-3/2)/(-13/2), true
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In (0,6), pick x=1. (4/2)<(-3/-5), false
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In (6,inf), pick x=7, (28)/(8)<-21/1, false
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Solution: -1
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Cheers,
Stan H.
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