Question 201339: Solve the inequality
(-6x+2)/(3x^2+7) >0
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! (-6x+2) (3x^2+7) > 0
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lets solve eqn as if it were equal to zero
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(-6x+2) (3x^2 +7) = 0
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-6x+2 = 0
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-6x = -2
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x= + 1/3,,,,,zero
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3x^2 +7 =0
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3x^2 =-7
x^2 = -7/3
x= +/- 1.53 i,,,,imaginary therefore not a Real Number Solution
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The only Real answer is x= +1/3
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If we had solved this part of the problem with the inequality problem with the inequality sign, -6x+2 >0, the answer would be
x < 1/3.
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Lets check by picking test points on either side of + 1/3
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Smaller than + 1/3, use 0,
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substituting,,,(-6(0)+2)(3(0)^2 +7) = 2*7=14,,,,or 14 > 0 ,,,,ok
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Larger than +1/3 ,,,use 1
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subst,,,,,(-6(1)+2)(3(1)^2 +7) = (-4)(10) = -40,,,,or -40>0,,,,not true
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Therefore ,,,,,x< 1/3,,,,is valid answer
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