Question
dentify the property that justifies each step asked about in the answer area below. Line 1: , 1, left parenthesis, 9, plus, 8, x, right parenthesis Line 1: = 1(9+8x) Line 2: , 1, left parenthesis, 8, x, plus, 9, right parenthesis Line 2: = 1(8x+9) Line 3: , 8, x, plus, 9 Line 3: = 8x+9 Answer Attempt 1 out of 2 Line 1 to Line 2: Line 2 to Line 3:
Answers
Answered by
GPT-4o mini
Let's identify the justification for each step based on the transformation of the expressions:
**Line 1 to Line 2:**
- **Justification:** Commutative Property of Addition
- Explanation: The Commutative Property of Addition states that you can add numbers in any order. Here, \(9 + 8x\) is rearranged to \(8x + 9\).
**Line 2 to Line 3:**
- **Justification:** Distributive Property
- Explanation: When multiplying by \(1\) (as in \(1(8x+9)\)), you are effectively distributing \(1\) across the terms inside the parentheses, which simplifies to just \(8x + 9\).
So, to summarize:
- **Line 1 to Line 2:** Commutative Property of Addition
- **Line 2 to Line 3:** Distributive Property
**Line 1 to Line 2:**
- **Justification:** Commutative Property of Addition
- Explanation: The Commutative Property of Addition states that you can add numbers in any order. Here, \(9 + 8x\) is rearranged to \(8x + 9\).
**Line 2 to Line 3:**
- **Justification:** Distributive Property
- Explanation: When multiplying by \(1\) (as in \(1(8x+9)\)), you are effectively distributing \(1\) across the terms inside the parentheses, which simplifies to just \(8x + 9\).
So, to summarize:
- **Line 1 to Line 2:** Commutative Property of Addition
- **Line 2 to Line 3:** Distributive Property