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

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