## buttermequeasy 4 years ago |x + 2| + 16 = 14 x = −32 and x = −4 x = −4 and x = 0 x = 0 and x = 28 No solution

1. amistre64

you cant negate an absolute value

2. buttermequeasy

I know.

3. myininaya

\[|something| \neq negative something \]

4. amistre64

| | = -# not good

5. amistre64

sites still going slow

6. myininaya

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

7. buttermequeasy

???

8. becca18

|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

9. myininaya

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

10. myininaya

|something| is either positive or neutral

11. myininaya

|something| is never negative

12. becca18

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

13. myininaya

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

14. myininaya

| | represents distance

15. myininaya

distance is either positive or zero

16. myininaya

distance is never negative

17. becca18

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

18. myininaya

absolute value is the distance of some number to 0

19. myininaya

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

20. buttermequeasy

So the answer is no solution ?

21. becca18

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

22. myininaya

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

23. myininaya

|junk| is never negative

24. myininaya

\[|junk| \neq negative something \]

25. becca18

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

26. buttermequeasy

I know that an absolute value can never be negative!

27. myininaya

then what you know there is no solution

28. myininaya

to this equation you have

29. buttermequeasy

Okay, thank you. Just making sure.

30. myininaya

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

31. becca18

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

32. myininaya

no you cannot |junk| is never negative

33. myininaya

|x+2|=-2 has no solution

34. becca18

|dw:1318992395252:dw|

35. myininaya

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

36. becca18

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

37. myininaya

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

38. satellite73

\[|x-a|\] 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

39. becca18

I don't understand. but okay.

40. arathock

= means the same...

41. myininaya

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

42. arathock

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

43. myininaya

right |junk| is never negative

44. arathock

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

45. 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

46. 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.

47. amistre64

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