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 quantity zero factor property false statement

Explanation:

Step1: Analyze the equation transformation

We start with \(-4x+\frac{64}{7}y^{2}-z=\frac{1}{7}y^{2}-z\). To get to \(-4x + 9y^{2}=0\), we first simplify the \(y^{2}\) - terms. \(\frac{64}{7}y^{2}-\frac{1}{7}y^{2}=\frac{64 - 1}{7}y^{2}=9y^{2}\). Also, we can use the additive - cancellation property. The \(z\) terms on both sides of the equation \(-4x+\frac{64}{7}y^{2}-z=\frac{1}{7}y^{2}-z\) can be cancelled out by adding \(z\) to both sides.

Step2: Identify the property and quantity

The property used is the Additive Cancellation Property. The quantity added to both sides is \(z\).

Answer:

Additive Cancellation Property, Quantity: \(z\)