Question 201339
(-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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