Question

Identify the property that justifies each step asked about in the answer area below.
Line 1: , 6, left parenthesis, 3, plus, 10, x, right parenthesis
Line 1: =
6(3+10x)
Line 2: , 6, left parenthesis, 10, x, plus, 3, right parenthesis
Line 2: =
6(10x+3)
Line 3: , 60, x, plus, 18
Line 3: =
60x+18
Answer
Attempt 1 out of 2

Line 1 to Line 2:
Line 2 to Line 3:

Answer 1

Let's identify the properties at each step.

**Line 1 to Line 2:**
This step involves rearranging the terms within the parentheses. The property used here is the **Commutative Property of Addition**, which states that the order of addition does not change the sum. Thus, \(3 + 10x\) is equivalent to \(10x + 3\).

**Line 2 to Line 3:**
This step involves distributing the 6 across the terms inside the parentheses. The property used here is the **Distributive Property**, which states that \(a(b + c) = ab + ac\). Hence, \(6(10x + 3)\) becomes \(6 \times 10x + 6 \times 3\), resulting in \(60x + 18\).

So, the properties for each step are:
- From Line 1 to Line 2: **Commutative Property of Addition**
- From Line 2 to Line 3: **Distributive Property**