Question

Identify the property that justifies each step asked about in the answer area below.
Line 1: (x+10)(5+3x)
Line 2: =(x+10)(3x+5)
Line 3: (3x+5)(x+10)

Answer 1

Let's identify the properties that justify each step in the provided lines:

**Line 1 to Line 2:**
\[(x+10)(5+3x) \rightarrow (x+10)(3x+5)\]

**Justification:** Commutative Property of Addition
(You rearranged the terms inside the parentheses from \(5 + 3x\) to \(3x + 5\). This is allowed because the order of addition does not affect the sum.)

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**Line 2 to Line 3:**
\[(x+10)(3x+5) \rightarrow (3x+5)(x+10)\]

**Justification:** Commutative Property of Multiplication
(You rearranged the factors from \((x+10)(3x+5)\) to \((3x+5)(x+10)\). This is permitted since the order of multiplication does not affect the product.)

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In summary:
1. **Line 1 to Line 2:** Commutative Property of Addition
2. **Line 2 to Line 3:** Commutative Property of Multiplication