Question 109120
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<x<0
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Cheers,
Stan H.