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anonymous

  • one year ago

What is ax + z = aw − y , for a?

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  1. Astrophysics
    • one year ago
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    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
    • one year ago
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    Any idea how?

  3. anonymous
    • one year ago
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    No

  4. anonymous
    • one year ago
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    Well yes

  5. Astrophysics
    • one year ago
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    \[z+y=a(w-x)\] Notice since the left side both share an a

  6. Astrophysics
    • one year ago
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    right side*

  7. anonymous
    • one year ago
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    But how did you get z+y

  8. anonymous
    • one year ago
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    and not -y-z

  9. Astrophysics
    • one year ago
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    Oh I added +y instead of subtracting both sides by z just to make it look cleaner

  10. anonymous
    • one year ago
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    But is subtracting both sides by z okay

  11. Astrophysics
    • one year ago
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    Does that make sense? |dw:1444601291806:dw|

  12. Astrophysics
    • one year ago
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    Yup, that's fine!

  13. Astrophysics
    • one year ago
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    With what you did, you should get \[ax-aw=-z-y\]

  14. anonymous
    • one year ago
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    but I got a = -y-z/x-w

  15. anonymous
    • one year ago
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    is that right?

  16. Astrophysics
    • one year ago
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    Yes!

  17. anonymous
    • one year ago
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    really?!

  18. anonymous
    • one year ago
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    it's not a = y+z/x-w

  19. Astrophysics
    • one year ago
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    \[ax-aw=-z-y \implies a(x-w) = -z-y \implies a = \frac{ -z-y }{ x-w }\] that's perfect :)

  20. anonymous
    • one year ago
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    ??

  21. anonymous
    • one year ago
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    How?

  22. Astrophysics
    • one year ago
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    \[a = \frac{ -z-y }{ x-w }\] 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
    • one year ago
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    Do 2 negatives always = a positive in algebra?

  24. Astrophysics
    • one year ago
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    yes :)

  25. anonymous
    • one year ago
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    Even if they are not side by side

  26. anonymous
    • one year ago
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    ?

  27. Astrophysics
    • one year ago
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    What do you mean

  28. anonymous
    • one year ago
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    like -5-5

  29. anonymous
    • one year ago
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    or is it only for variables?

  30. Astrophysics
    • one year ago
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    Oh there you're just adding -(5+5) = -(10) = -10

  31. Astrophysics
    • one year ago
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    Or subtracting by -5 how ever you like

  32. Astrophysics
    • one year ago
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    -5-5 = -10

  33. anonymous
    • one year ago
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    yeah

  34. Astrophysics
    • one year ago
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    Unless you mean (-5)(-5) = 25

  35. anonymous
    • one year ago
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    but how does -y-z = a positive?

  36. Astrophysics
    • one year ago
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    -5x-5 = 25

  37. Astrophysics
    • one year ago
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    (-y-z)*-1 = y+z

  38. anonymous
    • one year ago
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    How did you get -1? Was it from factoring the two a's in the equation?

  39. Astrophysics
    • one year ago
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    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
    • one year ago
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    so it could come out either way and be right?

  41. Astrophysics
    • one year ago
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    |dw:1444602123088:dw|

  42. Astrophysics
    • one year ago
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    Yes

  43. Astrophysics
    • one year ago
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    Now I'll do it again your way

  44. anonymous
    • one year ago
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    k

  45. Astrophysics
    • one year ago
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    |dw:1444602178558:dw|

  46. anonymous
    • one year ago
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    Thank you so much!

  47. Astrophysics
    • one year ago
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    Yw

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