# 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((:

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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

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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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