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boomerang285

  • 2 years ago

can someone show me the steps to solve x/6=x/7+5

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  1. carl_gauss
    • 2 years ago
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    multiply with 6 and 7 than bring x to one side. voila

  2. boomerang285
    • 2 years ago
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    \[\frac{ x }{ 6 }=\frac{ x }{ 7 }+5\] to better understand here is the actual problem in the correct equation

  3. order
    • 2 years ago
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    Move the x's to one side. Make the denominators equal. Minus the two terms, and move the denominator over to the over side and multiply 5 by the denominator (42) and then divide by the number next to x on the side where 5(42) is. and voila

  4. order
    • 2 years ago
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    7x/42 - 6x/42 = 5 x/42=5 x=5(42)

  5. calculusfunctions
    • 2 years ago
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    \[\frac{ x }{ 6 }=\frac{ x }{ 7 }+5\] Multiply both sides by 42 (least common multiple of 6 and 7), to obtain 7x = 6x + 210 ∴ x = 210 Do you understand?

  6. boomerang285
    • 2 years ago
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    so step 2 would look like x/7-x/6=5

  7. order
    • 2 years ago
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    yes

  8. order
    • 2 years ago
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    Then you make the denominators the same

  9. boomerang285
    • 2 years ago
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    which would be 42,

  10. order
    • 2 years ago
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    yes since 6 X 7 = 42

  11. boomerang285
    • 2 years ago
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    this is the part i get confused at

  12. boomerang285
    • 2 years ago
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    would it look like x/42?

  13. order
    • 2 years ago
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    but in order to make the denominators equation, you need to times the numerator by the amount that the denominator needs to make 42. eg. 6 X ? = 42 (7) so times the top x by 7 which becomes 7x. and the other becomes 6x since you need to times 7 by 6 to make 42. so it would be 7x/42 - 6x/42 7x-6x = x so it will eventually become x/42

  14. boomerang285
    • 2 years ago
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    ahhh ok

  15. boomerang285
    • 2 years ago
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    so then is x/42=5

  16. order
    • 2 years ago
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    Yup

  17. boomerang285
    • 2 years ago
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    and then simplify from there

  18. order
    • 2 years ago
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    yup :)

  19. boomerang285
    • 2 years ago
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    how do i get x by itself?

  20. order
    • 2 years ago
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    move the 42 over to the other side by timesing both sides by 42.

  21. magepker728
    • 2 years ago
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    |dw:1349349298325:dw|

  22. order
    • 2 years ago
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    42(x/42) = 5(42) x =210

  23. boomerang285
    • 2 years ago
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    thank you so much.. fractions is one thing i have an issue with..

  24. order
    • 2 years ago
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    that's fine :)

  25. boomerang285
    • 2 years ago
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    i have even harder ones... like \[\frac{ x}{ 2x+2 }=\frac{ -2x }{ 4x+4 }+\frac{ 2x-3 }{ x+1 }\]

  26. order
    • 2 years ago
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    You use the same principle: so to add two fractions, the denominators must be the same. make the denominator under -2x simplified: 4x + 4 4(x+1) and use {-2x over 4(x+1)} + {4(2x-3) over 4(x+1)} as a first step

  27. order
    • 2 years ago
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    \[{-2x \over 4(x+1)} + {4(2x-3) \over 4(x+1)}\]

  28. order
    • 2 years ago
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    and add them \[-2x + 8x -12 \over 4(x+1)\]

  29. order
    • 2 years ago
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    do the same with the other side and use 2(x+1) as denominator

  30. order
    • 2 years ago
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    \[{x \over 2(x+1)} = {6x -12 \over 4(x+1)}\]

  31. order
    • 2 years ago
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    and cross multiply for simplification

  32. order
    • 2 years ago
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    2x(x+1) = (6x-12) (x+1)

  33. order
    • 2 years ago
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    cancel the x+1 and you have 2x = 6x-12

  34. order
    • 2 years ago
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    and that is simplified as -4x = -12 which means x = 3

  35. order
    • 2 years ago
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    understand?

  36. boomerang285
    • 2 years ago
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    i believe so

  37. order
    • 2 years ago
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    great :)

  38. boomerang285
    • 2 years ago
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    i have one more fraction if anyone is interested in helping

  39. boomerang285
    • 2 years ago
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    \[\frac{ 5 }{ y-4 }-\frac{ 8 }{ y-4 }=\frac{ 2 }{ y^2-16 }\]

  40. boomerang285
    • 2 years ago
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    it throws me off to add sqrt

  41. order
    • 2 years ago
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    um... you could do it like this: \[{-3 \over y-4} = {2 \over y^2 -16}\] \[{-3 \over y -4} = {2 \over (y+4)(y-4)}\]

  42. order
    • 2 years ago
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    Then knock off the y-4 so you're left with \[-3 = {2 \over y+4}\]

  43. order
    • 2 years ago
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    and then use -3 (y+4) = 2 and simplify -3y - 12 = 2 -3y = 2 +12 -3y = 14 y = 14/-3

  44. order
    • 2 years ago
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    y = -(14/3)

  45. boomerang285
    • 2 years ago
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    wow that was easier than i thought

  46. order
    • 2 years ago
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    You were only stumped by the y^2 - 16 which is simplified as (y-4)(y+4)

  47. boomerang285
    • 2 years ago
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    thank you so much for helping me with these!

  48. order
    • 2 years ago
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    No probelma :)

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