Question

Identify the property that justifies each step asked about in the answer area below. Line 1: , left parenthesis, minus, 8, plus, 4, x, right parenthesis, plus, 9 Line 1: = (−8+4x)+9 Line 2: , left parenthesis, 4, x, plus, left parenthesis, minus, 8, right parenthesis, right parenthesis, plus, 9 Line 2: = (4x+(−8))+9 Line 3: , 4, x, plus, left parenthesis, minus, 8, plus, 9, right parenthesis Line 3: = 4x+(−8+9) Line 4: , 4, x, plus, 1 Line 4: = 4x+1 Answer Attempt 1 out of 2 Line 1 to Line 2: Line 2 to Line 3:

Answer 1

Let's examine the steps and the properties that justify the transitions from one line to another:

**Line 1 to Line 2:**
- **Property:** **Associative Property of Addition**
- Justification: The expression can be regrouped without changing its value. The parentheses indicate a rearrangement of terms: (−8 + 4x) is regrouped to (4x + (−8)).

**Line 2 to Line 3:**
- **Property:** **Commutative Property of Addition**
- Justification: The order of addition can be changed. The expression (4x + (−8)) becomes (−8 + 9) while keeping the value the same.

To summarize:
- Line 1 to Line 2: **Associative Property of Addition**
- Line 2 to Line 3: **Commutative Property of Addition**