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Math Help - "Solving Equations with Variables on Both Sides"

  1. #1
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    "Solving Equations with Variables on Both Sides"

    alright, heres the story. we had some homework assigned on the above subject, on a day i wasnt there. i missed the lesson, needless to say, and now have the weekend to learn it before a pretest. ive got a week to do the homework because i missed the day, but i still have to do the pretest. so, can someone give me a crash course on Solving Equations with Variables on Both Sides?
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  2. #2
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    Ok let's say we have 2x - 1 = 3x - 5

    Then let's try to get the x's and the numbers on different sides. In this case we will subtract the 2x from the left and right and add the 5 to the left and right then we will get our conclusion.

    4 = x You can always plug that value back into the equation to make sure you got it right.

    Here are a few others you can try.

    5x + 1 = 8x - 8
    9x + 12 = 5x + 16 (There's a little bit of a shortcut on this one see if you can notice it)
    4x - 3 = 2x + 1
    11x + 20 = 13x - 10


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  3. #3
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    Quote Originally Posted by SnipedYou View Post
    Ok let's say we have 2x - 1 = 3x - 5


    Then let's try to get the x's and the numbers on different sides. In this case we will subtract the 2x from the left and right and add the 5 to the left and right then we will get our conclusion.

    4 = x You can always plug that value back into the equation to make sure you got it right.

    Here are a few others you can try.

    5x + 1 = 8x - 8
    9x + 12 = 5x + 16 (There's a little bit of a shortcut on this one see if you can notice it)
    4x - 3 = 2x + 1
    11x + 20 = 13x - 10

     5x + 1 = 8x - 8
    subtract 5x from both sides, leaving 1 = 3x-8..
    then add 8 to each side, leaving 9=3x, and divide each side by 3, which is 3=x
    9x + 12 = 5x + 16subtract 5x from both sides, 4x+12=16, subtract 12 from each side, leaving 4x=4, divide each side by 4, leaving x=1.
    4x - 3 = 2x + 1
    subtract 2x from each side, leaving 2x-3 = 1
    add 3 to each side, leaving 2x=4
    divide each side by 2, x=2.
    11x + 20 = 13x - 10
    subtract 11x from both sides..20=2x-10
    add 10 to each side..30=2x
    divide each side by 2, 15=x

    i think i got it, pretty easy..thanks
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  4. #4
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    Yup you got it.

    Just so you know the shortcut I was getting at. Notice that 9 + 12 = 5 + 16 therefore x = 1. Its always good to check by solving though.
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  5. #5
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    Ah, was wondering that. cool, now to do the homework...lol
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