Question

choose the property of addition that justifies the equation.
(3 + y) + 8 = 3 + (y + 8) select
0 = -6 + 6 select
5 + a = a + 5 select

Explanation:

Step1: Analyze \((3 + y) + 8 = 3 + (y + 8)\)

The associative property of addition states that \((a + b) + c = a + (b + c)\). Here, \(a = 3\), \(b = y\), \(c = 8\), so this equation uses the Associative Property of Addition.

Step2: Analyze \(0=-6 + 6\)

The additive inverse property states that for any number \(a\), \(a+(-a)=0\) (or \(-a + a = 0\)). Here, \(a = 6\), so \(-6+6 = 0\) uses the Additive Inverse Property.

Step3: Analyze \(5 + a=a + 5\)

The commutative property of addition states that \(a + b = b + a\). Here, \(a = 5\), \(b = a\) (the variable), so this equation uses the Commutative Property of Addition.

Answer:

1. For \((3 + y) + 8 = 3 + (y + 8)\): Associative Property of Addition
2. For \(0=-6 + 6\): Additive Inverse Property
3. For \(5 + a=a + 5\): Commutative Property of Addition