(3x-2)/(4x-7)(1-3x)/(5-4x)

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Solution for (3x-2)/(4x-7)(1-3x)/(5-4x) equation:


D( x )

5-(4*x) = 0

4*x-7 = 0

5-(4*x) = 0

5-(4*x) = 0

5-4*x = 0

5-4*x = 0 // - 5

-4*x = -5 // : -4

x = -5/(-4)

x = 5/4

4*x-7 = 0

4*x-7 = 0

4*x-7 = 0 // + 7

4*x = 7 // : 4

x = 7/4

x in (-oo:5/4) U (5/4:7/4) U (7/4:+oo)

(3*x-2)/(4*x-7) < (1-(3*x))/(5-(4*x)) // - (1-(3*x))/(5-(4*x))

(3*x-2)/(4*x-7)-((1-(3*x))/(5-(4*x))) < 0

(3*x-2)/(4*x-7)-((1-3*x)/(5-4*x)) < 0

(3*x-2)/(4*x-7)+(-1*(1-3*x))/(5-4*x) < 0

((3*x-2)*(5-4*x))/((4*x-7)*(5-4*x))+(-1*(1-3*x)*(4*x-7))/((4*x-7)*(5-4*x)) < 0

(3*x-2)*(5-4*x)-1*(1-3*x)*(4*x-7) < 0

-2*x-3 < 0

(-2*x-3)/((4*x-7)*(5-4*x)) < 0

(-2*x-3)/((4*x-7)*(5-4*x)) < 0 // * ((4*x-7)*(5-4*x))^2

(-2*x-3)*(4*x-7)*(5-4*x) < 0

( -2*x-3 )

-2*x-3 < 0 // + 3

-2*x < 3 // : -2

x > 3/(-2)

x > -3/2

( 4*x-7 )

4*x-7 < 0 // + 7

4*x < 7 // : 4

x < 7/4

( 5-4*x )

5-4*x < 0 // - 5

-4*x < -5 // : -4

x > -5/(-4)

x > 5/4

(-oo:-3/2) (-3/2:5/4) (5/4:7/4) (7/4:+oo) -2*x-3 + - - - 4*x-7 - - - + 5-4*x + + - -

x in (-oo:-3/2) U (5/4:7/4)

(-oo:-3/2) U (5/4:7/4)

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