Question

choose the property of addition that justifies the equation.
0 = -6 + 6
select
3 + (9 + b) = (3 + 9) + b
select
5 + 0 = 5
select

Explanation:

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

Step1: Recall addition properties

The equation \( 0 = -6 + 6 \) shows that adding a number and its additive inverse (opposite) gives zero. The property is the Additive Inverse Property, which states that for any real number \( a \), \( a + (-a)=0 \) (or \( -a + a = 0 \)). Here, \( a = 6 \), so \( -6+6 = 0 \).

Second Equation: \( 3+(9 + b)=(3 + 9)+b \)

Step1: Recall addition properties

The equation \( 3+(9 + b)=(3 + 9)+b \) shows that the way we group three numbers when adding does not change the sum. This is the Associative Property of Addition, which states that for any real numbers \( a \), \( b \), and \( c \), \( (a + b)+c=a+(b + c) \). Here, \( a = 3 \), \( b = 9 \), and \( c = b \), so \( 3+(9 + b)=(3 + 9)+b \) follows the Associative Property of Addition.

Third Equation: \( 5 + 0 = 5 \)

Step1: Recall addition properties

The equation \( 5+0 = 5 \) shows that adding zero to a number does not change the number. This is the Additive Identity Property, which states that for any real number \( a \), \( a + 0=a \) (or \( 0 + a=a \)). Here, \( a = 5 \), so \( 5+0 = 5 \) follows the Additive Identity Property.

Answer:

s:

• For \( 0 = -6 + 6 \): Additive Inverse Property
• For \( 3+(9 + b)=(3 + 9)+b \): Associative Property of Addition
• For \( 5 + 0 = 5 \): Additive Identity Property