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Math Help - Solving for 'x'

  1. #1
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    Solving for 'x'

    (x+4)/2 = (x-3)/3

    I know you need to multiply both sides by the Least common multiple for the denominator, but then I get lost. please help me.
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  2. #2
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    (x+4)/2 = (x-3)/3

    you can cross multiply

    3(x+4) = 2(x-3)

    3x + 12 = 2x - 6
    3x = 2x -18
    (3x/2x) = -18
    the x cancels out and your left with
    3 = -18 which is not true

    your original statement is false
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  3. #3
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    Okay, but then what would I do for this one when I need to find the least common multiple?

    2/3x + 1/2 = 5/6x

    I know the LCM is 6, but not sure what goes on after that. I have been doing math all day and really just drawing blanks now. Please explain to me the steps.
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  4. #4
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    2/3x + 1/2 = 5/6x

    No problem.

    First, get all the x's in the same multiple. 3 and 6 are similar so this isnt too difficult.

    3 * 2 = 6 so write 2/3 as 2(2)/3(2) or 4/6
    because 2/3 = 4/6

    4/6x + 1/2 = 5/6x
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  5. #5
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    Nothing happened to the 1/2?
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  6. #6
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    nope, it can stay unless you choose to rewrite it.
    heres something you can use

    1/2 = n/6
    2n = 6
    n = 3

    1/2 = 3/6
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  7. #7
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    Thumbs up Just clarifying

    Quote Originally Posted by Dubulus View Post
    (x+4)/2 = (x-3)/3

    you can cross multiply

    3(x+4) = 2(x-3)

    3x + 12 = 2x - 6
    3x = 2x -18
    (3x/2x) = -18
    the x cancels out and your left with
    3 = -18 which is not true

    your original statement is false
    Hi!
    I think that upto the third step u r right, after that that +2x has to come for the left side
    that is
    3x-2x=-18
    1x = -18
    x = -18
    The value of x got.
    I hope u may understood now
    ok bye.
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  8. #8
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by agentlopez View Post
    Okay, but then what would I do for this one when I need to find the least common multiple?

    2/3x + 1/2 = 5/6x

    I know the LCM is 6, but not sure what goes on after that. I have been doing math all day and really just drawing blanks now. Please explain to me the steps.
    Before I get going: Saranya is right, dubulus made an error when he divided by 2x (just clearing that up for agentlopez)


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

    The first thing I like to do is bring all the x's to the same side:

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

    Then you bring it all together:

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

    Now you need to subtract those two fractions from each other, so you need to find the least common multiple.

    \frac{1}{2} = \left( \frac{5}{6}-\frac{4}{6}\right) x

    Then you can put it all together:

    \frac{1}{2} = \frac{5-4}{6}x \quad\rightarrow\quad \frac{1}{2} = \frac{1}{6}x

    Then to solve for x, you have to divide away that 1/6:

    \frac{1}{2} \div \frac{1}{6}=x

    So now we cross multiply:

    \frac{1}{2} \nearrow\!\!\!\!\!\!\searrow\!\!\!\!\!\!\nwarrow \!\!\!\!\!\!\swarrow \frac{1}{6}=x

    and we get:

    \frac{6}{2}=x\quad\rightarrow\quad\boxed{x=3}
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  9. #9
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    Quote Originally Posted by Dubulus View Post
    2/3x + 1/2 = 5/6x

    No problem.

    First, get all the x's in the same multiple. 3 and 6 are similar so this isnt too difficult.

    3 * 2 = 6 so write 2/3 as 2(2)/3(2) or 4/6
    because 2/3 = 4/6

    4/6x + 1/2 = 5/6x
    hi
    just i am trying for u

    2/3x + 1/2 = 5/6x
    taking lcm on the left side

    4 + 3x/6x = 5/6x
    then.
    4 + 3x/6x - 5/6x = 0
    4 + 3x - 5/6x = 0
    3x -1/6x = 0
    3x -1 = 0
    3x = 0 + 1
    3x = 1
    x = 1/3
    may be the answer, ok.
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  10. #10
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    Just in case agentlopez is trying to figure out why people are giving different answers to the second problem, Quick clearly and correctly got x=3 out of



    and Saranya, also correctly, got x = 1/3 out of

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

    You should make sure you understand the post that solved the problem you were trying to ask.
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  11. #11
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    (x+4)/2 = (x-3)/3

    cross multiply, so you get:
    3(x+4) = 2(x-3)
    then expand the brackets:
    3x + 12 = 2x - 6
    then take the 2x to the left side and the 12 to the right side:
    3x - 2x = -6 - 12
    which give:
    x = -18
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