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

Mathematics
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first find when (x+1)/(2-x)=4 or is undefined
you will need these values to solve the inequality
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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
Sorry....but may u do it?
(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
now we can split the number line up into 3 intervals using these 2 numbers
first we will simplify the rational inequality
well i guess that's not necessary in this case, but usually you want to get 0 on one side of the inequality
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)
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
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
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
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
Thanks for the answer

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