Question

choose the property of addition that justifies the equation.
$b = b + 0$ select
$6 + (-6) = 0$ select
$8 + y = y + 8$ select

Explanation:

First Equation: \( b = b + 0 \)

Step1: Recall Addition Properties

The additive identity property states that adding 0 to a number (or variable) does not change the number. The formula for the additive identity property is \( a + 0 = a \) (or \( a = a + 0 \), which is the same).

Step2: Match with the Equation

For the equation \( b = b + 0 \), we can see that adding 0 to \( b \) (on the right - hand side) results in \( b \) (on the left - hand side), which fits the additive identity property.

Step1: Recall Addition Properties

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

Step2: Match with the Equation

In the equation \( 6 + (-6)=0 \), \( a = 6 \) and its additive inverse is \( - 6 \), and their sum is 0, so this follows the additive inverse property.

Step1: Recall Addition Properties

The commutative property of addition states that for any two numbers (or variables) \( a \) and \( b \), \( a + b=b + a \).

Step2: Match with the Equation

In the equation \( 8 + y=y + 8 \), \( a = 8 \) and \( b = y \), and we can see that the order of addition is changed but the result remains the same, which fits the commutative property of addition.

Answer:

Additive Identity Property

Second Equation: \( 6+(-6) = 0 \)