SOLUTION: Solve x-6>(2/x)

Question 525904: Solve x-6>(2/x)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1Solve x-6>(2/x)
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x cannot be zero.
solve x-6 = 2/x
x^2-6x-2 = 0
x = [6+-sqrt(36-4*-2)]/2
x = [6+-2sqrt(11)]/2
x = [3+-sqrt(11)]
x = -0.3166 or x = 6.3166
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Draw a number line and plot x = -0.3166, 0 and 6.3166 on it.
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Test a value from each of the 4 line intervals to see where
the solutions are.
x-6 > (2/x)
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Let x = -2 to get: (-2-6)>(-1) ; false
Let x = -0.2 to get: -6.2 > [2/(-0.2)] ; true so solutions in (-0.3166,0)
Let x = 0.2 to get: -5.8 > [2/0.2] false
Let x = 10 to get: 10-6 > 2/10 ; true so solutions in (6.3166,+oo)
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Conclusion: Solutions in (-0.3166,0)U(6.3166,+oo)
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cheers,
Stan H.
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