Question

choose the property of addition that justifies the equation.
$6 + \left(y + 4\
ight) = \left(6 + y\
ight) + 4$
$3 + 0 = 3$
$\left(5 + x\
ight) + 2 = 2 + \left(5 + x\
ight)$
select
commutative property
associative property
additive identity property
additive inverse property

Explanation:

For the equation \( 6 + (y + 4) = (6 + y) + 4 \):

Step1: Recall Addition Properties

The Associative Property of Addition states that for any real numbers \( a \), \( b \), and \( c \), \( a + (b + c) = (a + b) + c \). It focuses on the grouping of addends.

Step2: Match with the Equation

In \( 6 + (y + 4) = (6 + y) + 4 \), we have \( a = 6 \), \( b = y \), \( c = 4 \). The grouping of \( y \) and \( 4 \) (on the left) is changed to grouping \( 6 \) and \( y \) (on the right), which matches the form of the Associative Property.

For the equation \( 3 + 0 = 3 \):

Step1: Recall Addition Properties

The Additive Identity Property states that for any real number \( a \), \( a + 0 = a \) (or \( 0 + a = a \)). The number \( 0 \) is the additive identity.

Step2: Match with the Equation

Here, \( a = 3 \), and \( 3 + 0 = 3 \) follows the form \( a + 0 = a \), so it's the Additive Identity Property.

For the equation \( (5 + x) + 2 = 2 + (5 + x) \):

Step1: Recall Addition Properties

The Commutative Property of Addition states that for any real numbers \( a \) and \( b \), \( a + b = b + a \). It focuses on the order of addends.

Step2: Match with the Equation

In \( (5 + x) + 2 = 2 + (5 + x) \), we have \( a = (5 + x) \) and \( b = 2 \), and the order of \( (5 + x) \) and \( 2 \) is swapped, matching the form of the Commutative Property.

Answer:

s:

• For \( 6 + (y + 4) = (6 + y) + 4 \): Associative Property
• For \( 3 + 0 = 3 \): Additive Identity Property
• For \( (5 + x) + 2 = 2 + (5 + x) \): Commutative Property