How do you solve and write the following in interval notation: (x)/(x+1) ≤ (-4)/(3(x-4))xx+143(x4)?

1 Answer
Dec 10, 2017

See below

Explanation:

x/(x+1)≤−4/(3(x−4))xx+143(x4)

x/(x+1)+4/(3(x−4))≤0xx+1+43(x4)0

(3x(x-4)+4(x+1))/(3(x+1)(x−4))≤03x(x4)+4(x+1)3(x+1)(x4)0

(3x^2-8x+4)/(3(x+1)(x−4))≤03x28x+43(x+1)(x4)0

x_(1,2)=(-b+-sqrt(b^2-4ac))/(2a)x1,2=b±b24ac2a

Let: a=3; b=-8; c=4

x_(1,2)=(8+-sqrt(8^2-4*3*4))/(2*3)x1,2=8±8243423

x_(1,2)=(8+-sqrt(16))/(2*3)x1,2=8±1623

x_(1,2)=(8+-4)/(2*3)x1,2=8±423

x_1=2/3x1=23

x_2=2x2=2

((x-2/3)(x-2))/(3(x+1)(x−4))≤0(x23)(x2)3(x+1)(x4)0

enter image source here

We need to find when is function <=00
function is negative for:
x in (-1,2/3]uuu[2,4)x(1,23][2,4)