Discussion
If \((x + 5) + 7y\) is written as \(5 + (x + 7y)\), then which of the following property/properties of addition is/are being used?
Answer: D
The properties used are commutative and associative both.
Going from (x + 5) + 7y to 5 + (x + 7y) takes two steps:
\[ \begin{aligned} (x + 5) + 7y &= (5 + x) + 7y \quad \text{commutative} \\ &= 5 + (x + 7y) \quad \text{associative} \end{aligned} \]
The order of x and 5 changes, which is the commutative property, and the grouping changes, which is the associative property. No multiplication is distributed over addition, so the distributive property (B, C) plays no part, and commutativity alone (A) would not regroup the terms.
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