document.write( "Question 201339: Solve the inequality\r
\n" ); document.write( "\n" ); document.write( "(-6x+2)/(3x^2+7) >0 \n" ); document.write( "
Algebra.Com's Answer #151555 by RAY100(1637)\"\" \"About 
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(-6x+2) (3x^2+7) > 0
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\n" ); document.write( "lets solve eqn as if it were equal to zero
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\n" ); document.write( "(-6x+2) (3x^2 +7) = 0
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\n" ); document.write( "-6x+2 = 0
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\n" ); document.write( "-6x = -2
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\n" ); document.write( "x= + 1/3,,,,,zero
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\n" ); document.write( "3x^2 +7 =0
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\n" ); document.write( "3x^2 =-7
\n" ); document.write( "x^2 = -7/3
\n" ); document.write( "x= +/- 1.53 i,,,,imaginary therefore not a Real Number Solution
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\n" ); document.write( "The only Real answer is x= +1/3
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\n" ); document.write( "If we had solved this part of the problem with the inequality problem with the inequality sign, -6x+2 >0, the answer would be
\n" ); document.write( "x < 1/3.
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\n" ); document.write( "Lets check by picking test points on either side of + 1/3
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\n" ); document.write( "Smaller than + 1/3, use 0,
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\n" ); document.write( "substituting,,,(-6(0)+2)(3(0)^2 +7) = 2*7=14,,,,or 14 > 0 ,,,,ok
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\n" ); document.write( "Larger than +1/3 ,,,use 1
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\n" ); document.write( "subst,,,,,(-6(1)+2)(3(1)^2 +7) = (-4)(10) = -40,,,,or -40>0,,,,not true
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\n" ); document.write( "Therefore ,,,,,x< 1/3,,,,is valid answer\r
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