What value of z would make the expressions 4x−5y and (3y+2x)−z(4y−x) equivalent?

Answer 1

To find the value of z that would make the expressions 4x - 5y and (3y + 2x) - z(4y - x) equivalent, we can set the two expressions equal to each other:

4x - 5y = (3y + 2x) - z(4y - x)

Simplify both sides of the equation:

4x - 5y = 3y + 2x - 4zy + zx

Rearrange the terms:

4x - 2x - 5y - 3y = -4zy + zx - 4xy

Combine like terms:

2x - 8y = z(-4y + x - 4x)

Divide both sides by -4y + x - 4x:

(2x - 8y) / (-4y + x - 4x) = z

Simplify the denominator:

(2x - 8y) / (-4y - 3x) = z

Therefore, the value of z that would make the two expressions equivalent is (2x - 8y) / (-4y - 3x).

Answer 2

so whats the answer

Answer 3

The answer is (2x - 8y) / (-4y - 3x).

Answer 4

the 2 equations are a fraction together

Answer 5

I apologize for the misunderstanding. If the two expressions are meant to be fractions, let's rewrite them accordingly:

First expression: (4x - 5y)
Second expression: [(3y + 2x) - z(4y - x)]

To find the value of z that would make these two fractions equivalent, we need to set them equal to each other:

(4x - 5y) = [(3y + 2x) - z(4y - x)]

To simplify, we can distribute the negative sign through z(4y - x):

4x - 5y = 3y + 2x - 4zy + zx

Now, let's isolate the terms involving z on one side of the equation:

4zy + zx = 2x - 3y - 4x + 5y

Combining like terms gives us:

xz + 4zy = -2x + 2y

Factoring out z:

z(x + 4y) = -2x + 2y

Now, divide both sides by (x + 4y) to solve for z:

z = (-2x + 2y) / (x + 4y)

Therefore, the value of z that would make the two fractions equivalent is (-2x + 2y) / (x + 4y).