calculus

The equation y = x(1/2) + 6 equals the equation y = x(1/3) + 12 at what value of x

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  1. that's EASY!! ((: just take what the y term equals, which is x(1/3) + 12 and replace the y value with that in the original equation!

    x(1/3) + 12 = x(1/2) + 6
    **&& I LOVE decimals more than factions so switch em' up!! ((:

    x(.3) + 12 = x (.5) + 6

    Move the x terms to the left & combine and the other terms to the right & combine! (: (you gotta multiply the x terms too! so .3x and .5x)

    .8x = 24

    then divide 24 by .8 annndddd((:

    TADA!! X=30!!

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  2. The above solution is not correct , even though miraculously tonya ended up with the right answer.

    we can write the equations as
    x/3 + 12 = x/2 + 6
    multiply by 6 , the common denominator to clear fractions
    2x + 36 = 3x + 6
    -x = -30
    x = 30

    There is no way tonya can come up with
    .8x = 24 from x(.3) + 12 = x(.5) + 6

    furthermore 1/3 ≠ .3

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  3. actually, as i was taught that using 1/3 as a decimal should just be .3 too & i see what tonya did! haha

    .8x comes from the addition of .3x+.5x. simple addition...

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  4. x/2 + 6 = x/3 + 1 2

    x/2 - x/3 = 12 - 6

    [ Remark: x/2 = 3x/6 and x/3 = 2x/6 ]

    3x/6 - 2x/6 = 6

    (3x - 2x)/6 = 6

    x/6 = 6 Multiply both sides with 6

    x = 36

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  5. Proof:

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

    36/2 + 6 = 36/3 + 12

    18 + 6 = 12 +12

    24 = 24

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