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anonymous

  • one year ago

I WILL GIVE MEDAL just help me please what are the solutions to this equation|x-10|-4=2x

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  1. Vocaloid
    • one year ago
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    the absolute value sign means we need to solve for two cases, one where (x-10) is positive and one where (x-10) is negative so we get: 1. x - 10 - 4 = 2x 2. -(x-10) - 4 = 2x solve each equation for x

  2. anonymous
    • one year ago
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    1. x - 10 - 4 = 2x do i add 4 with -4 and 2x?

  3. Vocaloid
    • one year ago
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    add 4 to both sides of the equal sign and tell me what you get

  4. anonymous
    • one year ago
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    1. x - 10 - 4 = 2x +4 +4 x-10=2x+4 is it like that?

  5. Vocaloid
    • one year ago
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    yes, now keep going

  6. anonymous
    • one year ago
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    Why not x - 10 - 4 = 2x -> x - 14 = 2x ?

  7. Vocaloid
    • one year ago
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    ^ that works, too

  8. anonymous
    • one year ago
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    Then subtract x from both sides

  9. campbell_st
    • one year ago
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    don't worry about that equation as it doesn't have a valid solution solve the other equation

  10. anonymous
    • one year ago
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    im still confuse with the first one..

  11. Vocaloid
    • one year ago
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    ok, we can pick up where you left off x-10=2x+4 now add 10 to both sides

  12. anonymous
    • one year ago
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    x=2x+14 is it like that?

  13. Vocaloid
    • one year ago
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    right, now subtract 2x from both sides

  14. anonymous
    • one year ago
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    x=2x+14 -2x -2x x=12x

  15. Vocaloid
    • one year ago
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    not quite, remember that you can't combine 14 since there's no x attached to it x - 2x = ?

  16. anonymous
    • one year ago
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    oh ok so its x-2x=14-2x

  17. Vocaloid
    • one year ago
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    almost x-2x = 2x+14-2x now keep going x - 2x = ?

  18. anonymous
    • one year ago
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    12

  19. Vocaloid
    • one year ago
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    nope 1-2 = ?

  20. anonymous
    • one year ago
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    -1

  21. Vocaloid
    • one year ago
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    right, so if 1-2 = -1, what does x - 2x = ?

  22. anonymous
    • one year ago
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    -x

  23. Vocaloid
    • one year ago
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    correcto, now we have -x = 2x+14-2x what is 2x+14-2x?

  24. anonymous
    • one year ago
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    im not sure

  25. Vocaloid
    • one year ago
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    hint: 2x - 2x = ?

  26. anonymous
    • one year ago
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    0

  27. Vocaloid
    • one year ago
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    good, so what is 2x+14-2x?

  28. anonymous
    • one year ago
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    0

  29. Vocaloid
    • one year ago
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    not quite... 2x+14-2x = 2x-2x+14 = ?

  30. anonymous
    • one year ago
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    It may be easier if it's re written as 2x - 2x + 14 = ?

  31. anonymous
    • one year ago
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    @Vocaloid never mind I didn't realize you wrote the same thing

  32. anonymous
    • one year ago
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    12

  33. Vocaloid
    • one year ago
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    nope, not quite.. 2x - 2x = 0 2x - 2x + 14 = ?

  34. anonymous
    • one year ago
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    2x - 2x + 14 => 0 + 14

  35. anonymous
    • one year ago
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    14

  36. Vocaloid
    • one year ago
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    right, that gives us -x = 14, which makes x = -14. (this solution doesn't quite work, like campbell mentioned, we'll see why later) now on to the second equation ~

  37. Vocaloid
    • one year ago
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    -(x-10) - 4 = 2x

  38. anonymous
    • one year ago
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    -(x-10) - 4 = 2x -x+10-4=2x

  39. Vocaloid
    • one year ago
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    good, keep going 10-4 = ?

  40. anonymous
    • one year ago
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    6

  41. Vocaloid
    • one year ago
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    good, that gives us -x + 6 = 2x now add x to each side

  42. anonymous
    • one year ago
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    -x + 6 = 2x +x +x -x+6x+2x+x

  43. Vocaloid
    • one year ago
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    not quite, remember that you can't combine numbers and variables -x + x + 6 = 2x + x

  44. Vocaloid
    • one year ago
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    now keep going -x + x + 6 = ?

  45. anonymous
    • one year ago
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    6

  46. Vocaloid
    • one year ago
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    excellent! now, x + 2x = ?

  47. anonymous
    • one year ago
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    2x

  48. Vocaloid
    • one year ago
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    nope, here's a hint: 1 + 2 = 3 x + 2x = ?

  49. anonymous
    • one year ago
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    3x

  50. Vocaloid
    • one year ago
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    good, now we have 3x = 6 now divide both sides by 3

  51. anonymous
    • one year ago
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    x=2

  52. Vocaloid
    • one year ago
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    good, we're almost done after solving the two equations we have x = -14 and x = 2 our next step is to substitute back into the original equation to see which ones work and which ones don't when we plug in x = -14, we get |x-10|-4=2x |-14-10|-4 = 2(-14) |-24|-4 = -28 24 - 4 = -28 20 = -28 (this is not true, so x = -14 is not our solution)

  53. Vocaloid
    • one year ago
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    next, we try x = 2 |x-10|-4=2x |2-10| -4 = 2(2) |-8| - 4 = 4 8 - 4 = 4 4 = 4 this is true, so x = 2 is our only solution

  54. anonymous
    • one year ago
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    ohh ok

  55. anonymous
    • one year ago
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    so it's x=-14 and x=2

  56. dm91
    • one year ago
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    i would say it is because of the work that you guys did up above but if not i will go back through it with you.

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