Question
Identify the property that justifies each step asked about in the answer area below. Line 1: 10(3+2x) line 2: 10(2x+3) line 3: 20x+30. line one to line is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property. Line 2 to line 3 is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property
Answers
GPT-4o mini
To identify the properties that justify the steps between the lines, let's analyze each line:
**Line 1 to Line 2:**
- Line 1: \(10(3 + 2x)\)
- Line 2: \(10(2x + 3)\)
The transition from Line 1 to Line 2 involves rearranging the terms inside the parentheses. This is justified by the **Commutative Property of Addition**, which states that \(a + b = b + a\).
**Line 2 to Line 3:**
- Line 2: \(10(2x + 3)\)
- Line 3: \(20x + 30\)
The transition from Line 2 to Line 3 involves distributing \(10\) across the terms inside the parentheses. This is justified by the **Distributive Property**, which states that \(a(b + c) = ab + ac\).
In summary:
- Line 1 to Line 2: **Commutative Property of Addition**
- Line 2 to Line 3: **Distributive Property**
**Line 1 to Line 2:**
- Line 1: \(10(3 + 2x)\)
- Line 2: \(10(2x + 3)\)
The transition from Line 1 to Line 2 involves rearranging the terms inside the parentheses. This is justified by the **Commutative Property of Addition**, which states that \(a + b = b + a\).
**Line 2 to Line 3:**
- Line 2: \(10(2x + 3)\)
- Line 3: \(20x + 30\)
The transition from Line 2 to Line 3 involves distributing \(10\) across the terms inside the parentheses. This is justified by the **Distributive Property**, which states that \(a(b + c) = ab + ac\).
In summary:
- Line 1 to Line 2: **Commutative Property of Addition**
- Line 2 to Line 3: **Distributive Property**