## viniterranova 3 years ago (x +1) / (2-x) < 4

1. Dockworker

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

2. Dockworker

you will need these values to solve the inequality

3. viniterranova

4. viniterranova

5. Dockworker

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

6. viniterranova

Sorry....but may u do it?

7. Dockworker

(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

8. Dockworker

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

9. Dockworker

first we will simplify the rational inequality

10. Dockworker

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

11. Dockworker

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)

12. Dockworker

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

13. Dockworker

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

14. Dockworker

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

15. Dockworker

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

16. viniterranova