Solve for x and y where needed
A.4([1]/[2]x + 2)=2([2]/[3]x - 3)
B.[3x -6]/[2y]=4........equation one
[2y+3]/[4]=2x
Keys- [numerator]/[denominator]
Using somewhat more conventional notation, we have
4((1/2)x+2) = 2((2/3)x-3)
2x+8 = (4/3)x-6
(2/3)x = -14
x = -21
(3x-6)/(2y) = 4
3x-6 = 8y
3x-8y = 6
(2y+3)/4 = 2x
2y+3 = 8x
8x-2y = 3
Doing a little scaling, that's the same as
3x-8y = 6
32x-8y = 12
Now subtract and you have
29x = 6
x = 6/29
and now you can find y = -39/58
To solve for x and y in each of the given equations, we will follow the steps below:
A. 4([1]/[2]x + 2) = 2([2]/[3]x - 3)
First, let's simplify the equation by eliminating the fractions. To do this, we can multiply every term in the equation by the least common multiple (LCM) of the denominators.
The LCM of 2 and 3 is 6. Multiply each term by 6 to clear the fractions:
4 * 6 * ([1]/[2]x + 2) = 2 * 6 * ([2]/[3]x - 3)
Simplifying further:
6([1]/[2]x + 2) = 12([2]/[3]x - 3)
Now distribute the multiplication:
6 * [1]/[2]x + 6 * 2 = 12 * [2]/[3]x - 12 * 3
Simplifying again:
[6/2]x + 12 = [24/3]x - 36
Simplifying the fractions:
3x + 12 = 8x - 36
To isolate the x term on one side, we need to eliminate the constant term from the other side. Let's subtract 8x from both sides:
3x - 8x + 12 = 8x - 8x - 36
Simplifying:
-5x + 12 = -36
Next, let's isolate the x term by subtracting 12 from both sides:
-5x + 12 - 12 = -36 - 12
Simplifying:
-5x = -48
Finally, solve for x by dividing both sides by -5:
x = -48 / -5
x = 9.6
Now that we have the value of x, we can substitute it back into the original equation to solve for y.
Let's use equation B to solve for y:
[3x - 6]/[2y] = 4
Replace x with its value:
[3 * 9.6 - 6]/[2y] = 4
Simplify:
[28.8 - 6]/[2y] = 4
Combine like terms:
22.8/[2y] = 4
To isolate y, we need to eliminate the fraction. Multiply both sides by 2y:
22.8 = 4 * 2y
Simplify:
22.8 = 8y
Divide both sides by 8 to solve for y:
y = 22.8 / 8
y = 2.85
So the solutions for x and y in the given equations are:
A. x = 9.6, y = 2.85