Solved on Oct 26, 2023

Determine if the statement is false or identify the property that justifies it. If cancellation is used, specify the quantity added/multiplied to both sides. $-4x + 14y^6 - z = 8y^6 - z \Leftrightarrow -4x + 6y^6 = 0$

STEP 1

Assumptions1. The given statement is-4 x+14 y^{6}-z=8 y^{6}-z \eftrightarrow-4 x+6 y^{6}=0. We need to identify if this statement is false or if it is justified by a mathematical property. If it is justified by a mathematical property, we need to identify which property it is and the quantity that is added to or multiplied by both sides.

STEP 2

Let's first simplify the given statement to see if it is true or false.
The given statement is equivalent to two equations $-4 x+14 y^{6}-z=8 y^{6}-z$ $-4 x+6 y^{6}=0$

STEP 3

Let's subtract $8y^{6}-z$ from both sides of the first equation to see if it simplifies to the second equation.
$(- x+14 y^{6}-z) - (8 y^{6}-z) =0$

STEP 4

implify the left-hand side of the equation.
$-4x +14y^{6} - z -8y^{6} + z = -4x +6y^{6}$

STEP 5

As you can see, the left-hand side of the equation simplifies to $-4x +y^{}$ , which is the left-hand side of the second equation. Therefore, the given statement is true.

STEP 6

Now, let's identify the property that justifies this transformation. In this case, we subtracted the same quantity, $8y^{6}-z$ , from both sides of the equation. This is justified by the Additive Cancellation Property.

STEP 7

The quantity that is added to or multiplied by both sides in this case is $- (y^{6}-z)$ .
So, the answer is Additive Cancellation Property and the quantity is $y^{6}-z$ .

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Determine if the statement is false or identify the property that justifies it. If cancellation is used, specify the quantity added/multiplied to both sides. $-4x + 14y^6 - z = 8y^6 - z \Leftrightarrow -4x + 6y^6 = 0$

STEP 1

STEP 2

Let's first simplify the given statement to see if it is true or false.
The given statement is equivalent to two equations $-4 x+14 y^{6}-z=8 y^{6}-z$ $-4 x+6 y^{6}=0$

STEP 3

Let's subtract $8y^{6}-z$ from both sides of the first equation to see if it simplifies to the second equation.
$(- x+14 y^{6}-z) - (8 y^{6}-z) =0$

STEP 4

implify the left-hand side of the equation.
$-4x +14y^{6} - z -8y^{6} + z = -4x +6y^{6}$

STEP 5

As you can see, the left-hand side of the equation simplifies to $-4x +y^{}$ , which is the left-hand side of the second equation. Therefore, the given statement is true.

STEP 6

Now, let's identify the property that justifies this transformation. In this case, we subtracted the same quantity, $8y^{6}-z$ , from both sides of the equation. This is justified by the Additive Cancellation Property.

STEP 7

The quantity that is added to or multiplied by both sides in this case is $- (y^{6}-z)$ .
So, the answer is Additive Cancellation Property and the quantity is $y^{6}-z$ .

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Determine if the statement is false or identify the property that justifies it. If cancellation is used, specify the quantity added/multiplied to both sides. −4x+14y6−z=8y6−z⇔−4x+6y6=0-4x + 14y^6 - z = 8y^6 - z \Leftrightarrow -4x + 6y^6 = 0−4x+14y6−z=8y6−z⇔−4x+6y6=0

STEP 1

STEP 2

Let's first simplify the given statement to see if it is true or false.The given statement is equivalent to two equations−4x+14y6−z=8y6−z-4 x+14 y^{6}-z=8 y^{6}-z−4x+14y6−z=8y6−z−4x+6y6=0-4 x+6 y^{6}=0−4x+6y6=0

STEP 3

Let's subtract 8y6−z8y^{6}-z8y6−z from both sides of the first equation to see if it simplifies to the second equation.(−x+14y6−z)−(8y6−z)=0(- x+14 y^{6}-z) - (8 y^{6}-z) =0(−x+14y6−z)−(8y6−z)=0

STEP 4

implify the left-hand side of the equation.−4x+14y6−z−8y6+z=−4x+6y6-4x +14y^{6} - z -8y^{6} + z = -4x +6y^{6}−4x+14y6−z−8y6+z=−4x+6y6

STEP 5

As you can see, the left-hand side of the equation simplifies to −4x+y-4x +y^{}−4x+y, which is the left-hand side of the second equation. Therefore, the given statement is true.

STEP 6

Now, let's identify the property that justifies this transformation. In this case, we subtracted the same quantity, 8y6−z8y^{6}-z8y6−z, from both sides of the equation. This is justified by the Additive Cancellation Property.

STEP 7

The quantity that is added to or multiplied by both sides in this case is −(y6−z)- (y^{6}-z)−(y6−z).So, the answer is Additive Cancellation Property and the quantity is y6−zy^{6}-zy6−z.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine if the statement is false or identify the property that justifies it. If cancellation is used, specify the quantity added/multiplied to both sides. $-4x + 14y^6 - z = 8y^6 - z \Leftrightarrow -4x + 6y^6 = 0$

Let's first simplify the given statement to see if it is true or false.
The given statement is equivalent to two equations $-4 x+14 y^{6}-z=8 y^{6}-z$ $-4 x+6 y^{6}=0$

Let's subtract $8y^{6}-z$ from both sides of the first equation to see if it simplifies to the second equation.
$(- x+14 y^{6}-z) - (8 y^{6}-z) =0$

implify the left-hand side of the equation.
$-4x +14y^{6} - z -8y^{6} + z = -4x +6y^{6}$

As you can see, the left-hand side of the equation simplifies to $-4x +y^{}$ , which is the left-hand side of the second equation. Therefore, the given statement is true.

Now, let's identify the property that justifies this transformation. In this case, we subtracted the same quantity, $8y^{6}-z$ , from both sides of the equation. This is justified by the Additive Cancellation Property.

The quantity that is added to or multiplied by both sides in this case is $- (y^{6}-z)$ .
So, the answer is Additive Cancellation Property and the quantity is $y^{6}-z$ .