Question

choose the property of addition that justifies the equation.
6 = 0 + 6\tselect

• y + y = 0\tcommutative property

\t\tassociative property
2 + b = b + 2\tadditive identity property
\t\tadditive inverse property

Explanation:

For the equation \( 6 = 0 + 6 \):

Step1: Recall Additive Identity Property

The Additive Identity Property states that for any number \( a \), \( a + 0 = a \) (or \( 0 + a = a \)).

Step2: Match with the Given Equation

In the equation \( 6 = 0 + 6 \), we have \( a = 6 \) and it follows the form \( a = 0 + a \), which is consistent with the Additive Identity Property.

For the equation \( -y + y = 0 \):

Step1: Recall Additive Inverse Property

The Additive Inverse Property states that for any number \( a \), there exists an additive inverse \( -a \) such that \( a + (-a) = 0 \) (or \( -a + a = 0 \)).

Step2: Match with the Given Equation

In the equation \( -y + y = 0 \), we have \( a = y \) and its additive inverse \( -y \), and their sum is \( 0 \), which is consistent with the Additive Inverse Property.

For the equation \( 2 + b = b + 2 \):

Step1: Recall Commutative Property of Addition

The Commutative Property of Addition states that for any numbers \( a \) and \( b \), \( a + b = b + a \).

Step2: Match with the Given Equation

In the equation \( 2 + b = b + 2 \), we have \( a = 2 \) and \( b = b \) (the variable), and it follows the form \( a + b = b + a \), which is consistent with the Commutative Property of Addition.

Answer:

s:

• For \( 6 = 0 + 6 \): Additive Identity Property
• For \( -y + y = 0 \): Additive Inverse Property
• For \( 2 + b = b + 2 \): Commutative Property