SOLUTION: Solve the inequalities for x x/x-2>3x-4/x

Question 1054743: Solve the inequalities for x
x/x-2>3x-4/x
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x/x-2>3x-4/x
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x^2 > (x-2)(3x-4)
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x^2 > 3x^2 -10x + 8
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2x^2 - 10x + 8 < 0
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x^2 - 5x + 4 < 0
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(x-4)(x-1) < 0
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Draw a number line.
Plot x = 1 and x = 4
Check a value in each of the 3 line intervals to find the solution set.
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Check x = 0 gives:: -*- < 0 ; False
Check x = 2 gives:: -*+ < 0 ; True ; So, solutions in (1,4)
Check x = 5 gives:: +*+ < 0 : False
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Ans:: All Real x in the interval (1,4)
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Cheers,
Stan H.
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