## anonymous 4 years ago if y<-2, then |y+2|/(y+2)=? i do not get this at all can someone please explain this to me?? what am I suppose to do and why?

1. myininaya

$|y+2|=y+2 \text{ if } y+2>0 => y>-2$ $|y+2|=-(y+2) \text{ if } y+2<0 => y<-2$

2. myininaya

$\frac{-(y+2)}{y+2} =\frac{-1}{1}=-1$

3. amistre64

since its an inequality your output is a range of values

4. amistre64

top is always + and bottom always - so the results are going to be - as a result

5. anonymous

okay so what would you do if 14<x, then |14-x|=? I'm just confused how you know when to do -(14-x) or just (14-x)

6. amistre64

x is always grater than 14

7. amistre64

14-14 = 0 and everything gerter than that is just +

8. amistre64

greater than that

9. amistre64

...negative, but still the abs makes it positives

10. anonymous

I know but the solution is -14+x why did they choose to do -(14-x) instead of 14-x

11. anonymous

I must be missing something....

12. amistre64

say x is greater than 14, x=20 for example: 14-20=-6 but we cant HAVE a -6 equal to an | |

13. myininaya

$|14-x| =14-x \text{ if } 14-x>0$ $|14-x|=-(14-x) \text{ if } 14-x<0$

14. amistre64

so they chose the one that will match it

15. myininaya

we want the output to be postive

16. myininaya

if 14-x<0, then -(14-x)>-0

17. myininaya

that is 0 not -0

18. anonymous

ahhh so y<-2 we want the output to be negative?

19. amistre64

yes

20. myininaya

$y<-2 => y+2<0 => |y+2|=-(y+2) \text{ since y+2 is negative }$

21. anonymous

I think I get it now that you guys so much!!! you just kind of have to sample the equation

22. amistre64

yes, sample it to see what will make sense overall :)

23. myininaya

i like my way if x>0 then |x|=x if x<0 then |x|=-x (-x gives us postive output because x is negative)

24. myininaya

x>0 means x is positive while x<0 means x is negative