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D( x )
2*x-1 = 0
2*x-1 = 0
2*x-1 = 0
2*x-1 = 0 // + 1
2*x = 1 // : 2
x = 1/2
x in (-oo:1/2) U (1/2:+oo)
(9*x)/(2*x-1) < x // - x
(9*x)/(2*x-1)-x < 0
(9*x)/(2*x-1)+(-x*(2*x-1))/(2*x-1) < 0
9*x-x*(2*x-1) < 0
10*x-2*x^2 < 0
10*x-2*x^2 = 0
2*x*(5-x) = 0
5-x = 0 // - 5
-x = -5 // * -1
x = 5
2*x*(x-5) = 0
(2*x*(x-5))/(2*x-1) < 0
(2*x*(x-5))/(2*x-1) < 0 // * (2*x-1)^2
2*x*(x-5)*(2*x-1) < 0
( 2*x-1 )
2*x-1 < 0 // + 1
2*x < 1 // : 2
x < 1/2
( 2*x )
2*x+0 < 0 // - 0
2*x < 0 // : 2
x < 0/2
x < 0
( x-5 )
x-5 < 0 // + 5
x < 5
(-oo:0) (0:1/2) (1/2:5) (5:+oo) 2*x-1 - - + + 2*x - + + + x-5 - - - +
x in (-oo:0) U (1/2:5)
(-oo:0) U (1/2:5)
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