Question

(x +1) / (2-x) < 4

Answer 1

first find when (x+1)/(2-x)=4 or is undefined

Answer 2

you will need these values to solve the inequality

Answer 3

May this help you.

Answer 4

yes, i know that is the question, but it is important that you solve the equation
(x+1)/(2-x)=4 before you solve (x+1)/(2-x)<4

Answer 5

Sorry....but may u do it?

Answer 6

(x+1)/(2-x)=4
x+1=4(2-x)
x+1=8-4x
5x=7
x=7/5
we also must know when (x+1)/(2-x)=4 is undefined
it is undefined at x=2, because the denominator 2-x=0

Answer 7

now we can split the number line up into 3 intervals using these 2 numbers

Answer 8

first we will simplify the rational inequality

Answer 9

well i guess that's not necessary in this case, but usually you want to get 0 on one side of the inequality

Answer 10

we have the values we will use to form our intervals, x=2, x=7/5
this splits the domain of the function into the following intervals:
(-infinity, 7/5), (7/5, 2), (2, infinity)

Answer 11

we will pick a value at random from these intervals and see if it is less than 4. if it is, the entire interval is part of the solution

Answer 12

from the first interval we can use x=0
(0+1)/(2-0)<4?
1/2<4? TRUE
x<7/5 is part of the solution

Answer 13

next we will pick the value 8/5 from the 2nd interval
(8/5+1)/(2-8/5)<4?
(13/5)/(2/5)<4?
13/2<4? FALSE, this is not part of solution

Answer 14

from 3rd interval we can use x=3
(3+1)/(2-3)<4?
4/-1<4?
-4<4? TRUE x>2 is part of solution
so entire solution is x<7/5 or x>2
now you see why we had to solve the related equation

Answer 15

Thanks for the answer