The equation y = x(1/2) + 6 equals the equation y = x(1/3) + 12 at what value of x
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!!
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
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...
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
Proof:
x/2 + 6 = x/3 + 1 2
36/2 + 6 = 36/3 + 12
18 + 6 = 12 +12
24 = 24
To find the value of x at which the two equations are equal, we need to set them equal to each other and solve for x.
Given equations:
y = x(1/2) + 6
y = x(1/3) + 12
Setting them equal:
x(1/2) + 6 = x(1/3) + 12
To eliminate the fractions, we can multiply both sides of the equation by a common multiple of the denominators (6 in this case).
6(x(1/2) + 6) = 6(x(1/3) + 12)
Distributing and simplifying:
3x + 36 = 2x + 72
Now, we can solve for x.
First, let's simplify the equation further:
3x - 2x = 72 - 36
x = 36
So the value of x at which the two equations are equal is 36.