Question

if the following statement is false, choose false statement. otherwise, identify the property that justifies it. if one of the cancellation properties is being used to transform the equation, identify the quantity that is added to or multiplied by both sides. -4x + \frac{64}{7}y^{2}-z = \frac{1}{7}y^{2}-z \leftrightarrow -4x + 9y^{2}=0 answer selecting an option will display any text boxes needed to complete your answer. multiplicative cancellation property additive cancellation property zero factor property false statement

Explanation:

Step1: Simplify left - hand side

Start with the left - hand side of the equation $-4x+\frac{64}{7}y^{2}-z$.

Step2: Simplify right - hand side

The right - hand side is $\frac{1}{7}y^{2}-z$.

Step3: Subtract $\frac{1}{7}y^{2}-z$ from both sides

$(-4x+\frac{64}{7}y^{2}-z)-(\frac{1}{7}y^{2}-z)=(-4x + 9y^{2})-0$.
$ - 4x+\frac{64}{7}y^{2}-z-\frac{1}{7}y^{2}+z=-4x + 9y^{2}$.
$ - 4x+(\frac{64 - 1}{7})y^{2}=-4x + 9y^{2}$.
$ - 4x+9y^{2}=-4x + 9y^{2}$, which is a true statement.
We can get from $-4x+\frac{64}{7}y^{2}-z=\frac{1}{7}y^{2}-z$ to $-4x + 9y^{2}=0$ by first subtracting $\frac{1}{7}y^{2}-z$ from both sides. This is an application of the additive cancellation property.

Answer:

Additive Cancellation Property