Select all that justify the following statement.3 + (y + 5) = y + 8commutative - multiplicationdistributivecommutative - additionassociative - additionassociative - multiplicationidentity - additionsymmetric
Question
Select all that justify the following statement.3 + (y + 5) = y + 8commutative - multiplicationdistributivecommutative - additionassociative - additionassociative - multiplicationidentity - additionsymmetric
Solution
To determine which properties justify the given statement, let's break it down step by step:
Step 1: 3 + (y + 5) = y + 8
Step 2: Using the commutative property of addition, we can rearrange the terms on the left side of the equation: (y + 5) + 3 = y + 8
Step 3: Now, using the associative property of addition, we can group the terms differently: y + (5 + 3) = y + 8
Step 4: Simplifying the terms in parentheses: y + 8 = y + 8
Step 5: Now, using the identity property of addition, we can see that both sides of the equation are equal: y + 8 = y + 8
Therefore, the properties that justify the given statement are:
- Commutative property of addition
- Associative property of addition
- Identity property of addition
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