x4x7 x1x4 Solve the nonlinear inequality x4x7 Solutionx4 x

(x+4)/(x+7) < (x-1)/(x-4)

Solve the nonlinear inequality. x+4/x+7

x+4 / x+7 < x-1/x-4

cross multiply

(x+4) (x-4) < (x-1) (x+7)

x^2 -16 < x^2 +7x -x -7

x^2 -16 <x^2 +6x -7

x^2 -16 -x^2 -6x +7 < 0

-16 -6x+7 < 0

-6x -9 < 0

-6x < 9

-x < 9/6

-x< 3/2

multiply with negative sign

-(-x) > -3/2

x > -3/2