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Math Help - I dont get it

  1. #1
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    I dont get it

    1. Solve: 2 5 1 - - - = -
    3 6 x

    Solution:
    The LCM of all denominators is
    6x. Multiply each side of the
    equation by 6x.

    6x((2/3) - (5/6)) = 6x(1/x)

    Use the distributive law of multi-
    plication, which says a(b + c) =
    ab + ac
    , to rewrite the
    equation.

    6x(2/3) - 6x(5/6) = 6x(1/x)

    Multiply each group of terms
    together.

    (12x/3) - 30x/6 = 6x/x

    Perform each of the indicated
    divisions.

    4x - 5x = 6

    Solve for x.
    Combine like terms.

    -x = 6

    Multiply each side by -1.

    x = -6

    Why would you Mutliply by 6X rather than just 6?
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  2. #2
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    Quote Originally Posted by Gordon View Post
    [B]1. Solve: 2 5 1 - - - = -
    3 6 x
    I can't follow this.
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  3. #3
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    Hello, Gordon!

    Doesn't anyone ever PREVIEW their posts?


    1. Solve: . \dfrac{2}{3} - \dfrac{5}{6} \;=\;\dfrac{1}{x}

    If you multiply through by 6 (only), you get:

    . . 6\,\bigg[\dfrac{2}{3} - \dfrac{5}{6} \;=\;\dfrac{1}{x}\bigg]  \quad\Rightarrow\quad 4 - 5 \;=\;\dfrac{6}{x}


    Now what?

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  4. #4
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    Yeah sorry about that, so So. Why do you mutliply by 6X in the first place that's part i don't get.
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  5. #5
    Senior Member eumyang's Avatar
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    Quote Originally Posted by Gordon View Post
    Yeah sorry about that, so So. Why do you mutliply by 6X in the first place that's part i don't get.
    Did you read Soroban's post?
    6\bigg[\dfrac{2}{3} - \dfrac{5}{6} \;=\;\dfrac{1}{x}\bigg] \quad\Rightarrow\quad 4 - 5 \;=\;\dfrac{6}{x}
    If you multiply by only 6, you will still have a fraction, with an x in the denominator. Now, the problem was to solve for x. You want to manipulate this equation so that you end with x = some number. It's a little more difficult to solve for x if it's in the denominator, isn't it?
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  6. #6
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    Yes, i saw his post, but the thing if i were to solve a problem i dont know if i would put an X with whatever number i got, for instant can you give me a problem simliar like that? and i'll try to solve it
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  7. #7
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    Quote Originally Posted by Gordon View Post
    Yes, i saw his post, but the thing if i were to solve a problem i dont know if i would put an X with whatever number i got, for instant can you give me a problem simliar like that? and i'll try to solve it
    Hi Gordon,

    other problems like this will require the same technique or a more complex variation.
    You should stay with it until you've got it...

    \frac{2}{3}-\frac{5}{6}=\frac{1}{x}

    You want to find the value of x, but it's in the denominator position.
    That's inconvenient,

    but \frac{x}{x}=1

    Both sides are equal, so if we multiply both sides by the same value,
    they will still be equal.
    Therefore multiply both sides by x
    since then we have an x no longer in the denominator position.

    Also multiply both sides by 6 to get rid of all fractions.
    Makes things much clearer as far as x is concerned.


    x\left(\frac{2}{3}-\frac{5}{6}\right)=\frac{x}{x}=1

    x6\left(\frac{2}{3}-\frac{5}{6}\right)=6

    x\left(6\frac{2}{3}-6\frac{5}{6}\right)=6

    x(4-5)=6

    x(-1)=6

    x=\frac{6}{-1}=-6
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  8. #8
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    Why not keep it simple:

    2/3 - 5/6 = 4/6 - 5/6 = -1/6

    So 1/x = -1/6 : x = -6
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  9. #9
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    Quote Originally Posted by Wilmer View Post
    Why not keep it simple:

    2/3 - 5/6 = 4/6 - 5/6 = -1/6

    So 1/x = -1/6 : x = -6
    cos the question was

    "why would you multiply by 6x rather than just 6"

    Anyway, I guess it's your round, Wilmer.
    I'll have a pint of Guinness, 2 mars bars and a Havana cigar. Thanks!!
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  10. #10
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    Quote Originally Posted by Archie Meade View Post
    cos the question was
    "why would you multiply by 6x rather than just 6"

    Wilmer: my way, multiplying as above is eliminated: so question would not be asked!

    Anyway, I guess it's your round, Wilmer.
    I'll have a pint of Guinness, 2 mars bars and a Havana cigar. Thanks!!

    Wilmer: I'll drink to that !! (and to that, and to that....)
    Mars bars with beer? YUK! Pickled wieners much better...
    .
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  11. #11
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    Thanks Archie, at first i couldn't get it, but after Wil. show me the simple way and i certain that i fully understand now so thanks to both of you
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