Question

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?

Answer 1

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

Answer 2

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

Answer 3

since its an inequality your output is a range of values

Answer 4

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

Answer 5

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)

Answer 6

x is always grater than 14

Answer 7

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

Answer 8

greater than that

Answer 9

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

Answer 10

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

Answer 11

I must be missing something....

Answer 12

say x is greater than 14, x=20 for example:

14-20=-6 but we cant HAVE a -6 equal to an | |

Answer 13

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

Answer 14

so they chose the one that will match it

Answer 15

we want the output to be postive

Answer 16

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

Answer 17

that is 0 not -0

Answer 18

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

Answer 19

yes

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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)

Answer 24

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