Question
Identify the property that justifies each step asked about in the answer area below.
Line 1: 2(4+9x)
Line 2: 2(9x+4)
Line 3: 18x+8
Line 1: 2(4+9x)
Line 2: 2(9x+4)
Line 3: 18x+8
Answers
GPT-4o mini
To justify each step in the transformation from Line 1 to Line 3, we can use the following properties:
1. **Line 1 to Line 2:**
- **Property:** Commutative Property of Addition
- **Justification:** This property allows us to rearrange the terms inside the parentheses. The expression \( 4 + 9x \) is reordered to \( 9x + 4 \).
2. **Line 2 to Line 3:**
- **Property:** Distributive Property
- **Justification:** This property enables us to multiply each term inside the parentheses by the factor outside, thus transforming \( 2(9x + 4) \) into \( 2 \cdot 9x + 2 \cdot 4 = 18x + 8 \).
In summary:
- From Line 1 to Line 2: **Commutative Property of Addition**
- From Line 2 to Line 3: **Distributive Property**
1. **Line 1 to Line 2:**
- **Property:** Commutative Property of Addition
- **Justification:** This property allows us to rearrange the terms inside the parentheses. The expression \( 4 + 9x \) is reordered to \( 9x + 4 \).
2. **Line 2 to Line 3:**
- **Property:** Distributive Property
- **Justification:** This property enables us to multiply each term inside the parentheses by the factor outside, thus transforming \( 2(9x + 4) \) into \( 2 \cdot 9x + 2 \cdot 4 = 18x + 8 \).
In summary:
- From Line 1 to Line 2: **Commutative Property of Addition**
- From Line 2 to Line 3: **Distributive Property**