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anonymous

  • 5 years ago

5+3[1+2(2x-3]=6(x+5)

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  1. sandra
    • 5 years ago
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    I'm assuming you mean 5+3(1+2(2x-3)) = 6(x+5)

  2. sandra
    • 5 years ago
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    this is another case where you need to distribute

  3. sandra
    • 5 years ago
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    start with the right side, what is 6(x+5) ?

  4. anonymous
    • 5 years ago
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    yes

  5. anonymous
    • 5 years ago
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    6x+30?

  6. sandra
    • 5 years ago
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    yep!

  7. sandra
    • 5 years ago
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    ok now start from the inside out on the left hand side

  8. anonymous
    • 5 years ago
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    do u always start with the right side

  9. sandra
    • 5 years ago
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    so what is 2(2x-3)

  10. sandra
    • 5 years ago
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    well, I think generally start from inside out

  11. sandra
    • 5 years ago
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    as in inner-most thing that needs to be expanded

  12. anonymous
    • 5 years ago
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    4x-6

  13. sandra
    • 5 years ago
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    ok great, so to recap, so far we have: 5 + 3(1 + 4x - 6) = 6x + 30

  14. anonymous
    • 5 years ago
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    gotcha

  15. sandra
    • 5 years ago
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    so to make it easier on yourself, how about combing like terms in the parens, so what is (1+4x - 6) ?

  16. anonymous
    • 5 years ago
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    5x-6 or do u break that down further

  17. sandra
    • 5 years ago
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    well, that's not correct

  18. sandra
    • 5 years ago
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    you can't combine 1 and 4x, since you don't know what 4x

  19. sandra
    • 5 years ago
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    but you can combine 1 and -6

  20. sandra
    • 5 years ago
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    (by adding them)

  21. anonymous
    • 5 years ago
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    -5

  22. sandra
    • 5 years ago
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    if it had been (1x +4x -6) you would have been correct, since the 1 and 4 are both x's

  23. sandra
    • 5 years ago
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    right so the middle is now -5 + 4x, or 4x - 5

  24. sandra
    • 5 years ago
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    so now you have : 5 + 3(4x - 5) = 6x + 30

  25. sandra
    • 5 years ago
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    what is your next step?

  26. anonymous
    • 5 years ago
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    5+12x-15=6x+30

  27. sandra
    • 5 years ago
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    great =)

  28. sandra
    • 5 years ago
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    so can you combine anything on the left side?

  29. anonymous
    • 5 years ago
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    5 and 15 which is -10

  30. sandra
    • 5 years ago
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    yep =), so now what do you have?

  31. anonymous
    • 5 years ago
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    is it 12x-10=6x+30

  32. sandra
    • 5 years ago
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    exactly

  33. sandra
    • 5 years ago
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    so now the basic rule of algebra, and equations/equalities in general - you can perform any operation to both sides of an equation and still have the equatoin be true (satisfied)

  34. sandra
    • 5 years ago
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    the reason that's powerful is because it allows you to eventually get x all by itself

  35. sandra
    • 5 years ago
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    so let's say you wanted to get 12x by itself on the left hand side

  36. sandra
    • 5 years ago
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    what could you add to both sides to make that happen?

  37. anonymous
    • 5 years ago
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    add 10

  38. sandra
    • 5 years ago
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    yep, and what do you get if you add 10 to both sides

  39. anonymous
    • 5 years ago
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    12x=6x+40

  40. sandra
    • 5 years ago
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    exactly. ok , so remember, when you're solving for a variable (in this case x), the idea is to get all of that variable to one side, and then eventually just one instance of that variable by itself (x)

  41. sandra
    • 5 years ago
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    so what could you subtract from both sides, to get all of the x's in one place?

  42. anonymous
    • 5 years ago
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    would u minus 6x

  43. sandra
    • 5 years ago
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    exactly, and then what you get?

  44. anonymous
    • 5 years ago
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    6x=40 then i divided by 6 both sides

  45. sandra
    • 5 years ago
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    yep!

  46. sandra
    • 5 years ago
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    good work

  47. anonymous
    • 5 years ago
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    6.6?

  48. sandra
    • 5 years ago
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    yeah, or you could write it as a fraction

  49. sandra
    • 5 years ago
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    so x = 40/6

  50. sandra
    • 5 years ago
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    and that can be reduced if you divide both top and bottom by 2

  51. sandra
    • 5 years ago
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    so x = 20/3

  52. sandra
    • 5 years ago
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    so now that you think x = 20/3

  53. anonymous
    • 5 years ago
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    thank u so much i think im getting it sum what lol

  54. sandra
    • 5 years ago
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    you stick it back into the original equation (or just use 6.666666 to check in your calculator)

  55. sandra
    • 5 years ago
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    and if the equation is true, then you know you got it right

  56. sandra
    • 5 years ago
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    so for these types of problems, try expanding everything out first

  57. sandra
    • 5 years ago
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    and then just keep doing the same operations on both sides until you conveniently get all the x's (or whatever you're solving for) in one place

  58. sandra
    • 5 years ago
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    and then just get the value for one x by dividing

  59. sandra
    • 5 years ago
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    after a while, you'll start seeing some shortcuts if they're there

  60. sandra
    • 5 years ago
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    for example, if you had 3(x+3) = 12

  61. sandra
    • 5 years ago
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    you wouldn't *have* to expand first

  62. sandra
    • 5 years ago
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    you could just divide both sides by 3

  63. sandra
    • 5 years ago
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    to get x+3 = 4

  64. sandra
    • 5 years ago
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    and then subtract 3 from both sides to get x=1

  65. sandra
    • 5 years ago
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    but seeing that will come with practice

  66. sandra
    • 5 years ago
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    good luck!

  67. anonymous
    • 5 years ago
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    oh ok thanks a bunch !!!!

  68. sandra
    • 5 years ago
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    yep np

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