anonymous one year ago What is ax + z = aw − y , for a?

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1. Astrophysics

You can do the following $z+y=aw-ax$ notice I added y on both sides and subtracted ax from both sides, now you can factor out an a.

2. Astrophysics

Any idea how?

3. anonymous

No

4. anonymous

Well yes

5. Astrophysics

$z+y=a(w-x)$ Notice since the left side both share an a

6. Astrophysics

right side*

7. anonymous

But how did you get z+y

8. anonymous

and not -y-z

9. Astrophysics

Oh I added +y instead of subtracting both sides by z just to make it look cleaner

10. anonymous

But is subtracting both sides by z okay

11. Astrophysics

Does that make sense? |dw:1444601291806:dw|

12. Astrophysics

Yup, that's fine!

13. Astrophysics

With what you did, you should get $ax-aw=-z-y$

14. anonymous

but I got a = -y-z/x-w

15. anonymous

is that right?

16. Astrophysics

Yes!

17. anonymous

really?!

18. anonymous

it's not a = y+z/x-w

19. Astrophysics

$ax-aw=-z-y \implies a(x-w) = -z-y \implies a = \frac{ -z-y }{ x-w }$ that's perfect :)

20. anonymous

??

21. anonymous

How?

22. Astrophysics

$a = \frac{ -z-y }{ x-w }$ or $a = \frac{ z+y }{ w-x }$ notice if you multiply the first equation by -1 you get the second equation, try to convince yourself by trying it

23. anonymous

Do 2 negatives always = a positive in algebra?

24. Astrophysics

yes :)

25. anonymous

Even if they are not side by side

26. anonymous

?

27. Astrophysics

What do you mean

28. anonymous

like -5-5

29. anonymous

or is it only for variables?

30. Astrophysics

Oh there you're just adding -(5+5) = -(10) = -10

31. Astrophysics

Or subtracting by -5 how ever you like

32. Astrophysics

-5-5 = -10

33. anonymous

yeah

34. Astrophysics

Unless you mean (-5)(-5) = 25

35. anonymous

but how does -y-z = a positive?

36. Astrophysics

-5x-5 = 25

37. Astrophysics

(-y-z)*-1 = y+z

38. anonymous

How did you get -1? Was it from factoring the two a's in the equation?

39. Astrophysics

Oh no I was trying to show you that the first equation is same as the second, all you have to do is multiply by -1, algebra doesn't care :P So the way I did your problem was basically the same way except I moved things differently, |dw:1444602003999:dw|

40. anonymous

so it could come out either way and be right?

41. Astrophysics

|dw:1444602123088:dw|

42. Astrophysics

Yes

43. Astrophysics

Now I'll do it again your way

44. anonymous

k

45. Astrophysics

|dw:1444602178558:dw|

46. anonymous

Thank you so much!

47. Astrophysics

Yw