|x + 2| + 16 = 14
x = −32 and x = −4
x = −4 and x = 0
x = 0 and x = 28
No solution

- buttermequeasy

|x + 2| + 16 = 14
x = −32 and x = −4
x = −4 and x = 0
x = 0 and x = 28
No solution

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- amistre64

you cant negate an absolute value

- buttermequeasy

I know.

- myininaya

\[|something| \neq negative something \]

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## More answers

- amistre64

| | = -# not good

- amistre64

sites still going slow

- myininaya

so what happens when you subtract 16 on both sides
don't we have |junk|=negative something?

- buttermequeasy

???

- anonymous

|x+2| +16=14
-16 -16
|x+2|=-2
x+2=-2
-2 -2
x=-4
I don't know how you got the second part but that's how i would do the first part

- myininaya

|x+2|=-2 never happens for any input

- myininaya

|something| is either positive or neutral

- myininaya

|something| is never negative

- anonymous

What do you mean?
you just drop you absolute value and subtract 2 on both sides to cancel out the 2 on the side with the variable.
and only |inside| has to positive..everything outside the | | can be whatever

- myininaya

we can put anything into | | and the output will either be 0 or positive

- myininaya

| | represents distance

- myininaya

distance is either positive or zero

- myininaya

distance is never negative

- anonymous

| | is called absolute value.. look it up on google.. Are you talking about highschool algebra or college?

- myininaya

absolute value is the distance of some number to 0

- myininaya

|-3|=3
|0|=0
|3|=3
|-141441|=141441
look the outputs are never negative

- buttermequeasy

So the answer is no solution
?

- anonymous

That's what i'm saying.. I didn't put a negative inside the bars i put them on the outside

- myininaya

butter ask yourself can you ever get a negative output for |something|
the answer is no

- myininaya

|junk| is never negative

- myininaya

\[|junk| \neq negative something \]

- anonymous

I know that... i didn't make |junk| negative it was still positive

- buttermequeasy

I know that an absolute value can never be negative!

- myininaya

then what you know there is no solution

- myininaya

to this equation you have

- buttermequeasy

Okay, thank you. Just making sure.

- myininaya

\[|x+2| \neq -2 \]

- anonymous

see there is no negative
except on the OTHERSIDE of the = sign.. and you can do that..

- myininaya

no you cannot
|junk| is never negative

- myininaya

|x+2|=-2 has no solution

- anonymous

|dw:1318992395252:dw|

- myininaya

|x+2| is positive or neutral
-2 is always negative
how could they ever be the same?

- anonymous

they are not the same... that's not a finished equation

- myininaya

|x+2| will never be the same as -2 for any x

- anonymous

\[|x-a|\] is the distance from x to a. for example
\[|5-8|=3\] because the distance between 5 and 8 is 3. as such, it cannot be negative. so if you ever see
\[|x-a|=-3\] for example, go get a snack and forget about trying to solve it. there is no solution to such a thing

- anonymous

I don't understand. but okay.

- anonymous

= means the same...

- myininaya

yes
= means we are looking for when two expressions are the same or meet or intersect

- anonymous

therefore |something|=something else means that even if the equation isn't finished it is still equal and therefore saying that |something|=negative something is wrong

- myininaya

right |junk| is never negative

- anonymous

you can say |-something|=something or -|something|=negative something or even -|-something|=negative something but you cant say |something|=negative something

- amistre64

or better yet, lets prove if Beccas result is good?
|x+2| +16=14
-16 -16
|x+2|=-2
x+2=-2
-2 -2
x=-4
lets assume x=-4 and use it in our equation.
|-4+2| +16=14
|-2| +16=14
2+16=14
18=14 .... this is a contradiction; so x cannot = -4

- amistre64

we can go even further and try to work this out like it would pop out a good result:
|x + 2| +16 = 14
-16 -16
----------------
|x+2| = -2
(x+2) = -2 or -(x+2) = -2
-2 -2 -x-2 = -2
+2 +2
--------------------------
x = -4 or -x = 0; or simply x=0
these are the only 2 possible solutions we can get from it; and we already tested x=-4 and it failed us. Lets test out x=0
|0 + 2| +16 = 14
|2| +16 = 14
2 +16 = 14
18 = 14 ... another bad result; since x cannot be the only 2 options that would naturally fit; the answer has to be that nothing will fit.

- amistre64

This is a redimentary proof that: |N| = -# is just plain false

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