The problem asks to identify the properties that justify each step in the given mathematical transformation.

The expressions in the lines are:

• Line 1: $(6 + x)x$
• Line 2: $x(6 + x)$
• Line 3: $x(x + 6)$

Step 1: Line 1 to Line 2

The transformation from Line 1 to Line 2 involves switching the terms inside the parentheses. This is the Commutative Property of Addition, which states that $a + b = b + a$. Here, $6 + x$ becomes $x + 6$.

Step 2: Line 2 to Line 3

The transformation from Line 2 to Line 3 involves applying the Commutative Property of Addition again inside the parentheses. The order of terms inside the parentheses has been reversed again: $6 + x$ becomes $x + 6$.

Therefore:

• Line 1 to Line 2: Commutative Property of Addition
• Line 2 to Line 3: Commutative Property of Addition

Would you like further details or have any questions about these steps?

Here are five related questions that might expand on this concept:

1. What is the difference between the commutative property of addition and multiplication?
2. Can the commutative property be applied to subtraction or division?
3. What is the associative property, and how is it different from the commutative property?
4. How would the associative property apply if the expression had more terms?
5. Are there any other properties that are commonly used in similar transformations?

Tip: Remember that the commutative property allows you to rearrange terms in addition and multiplication, but it doesn't apply to subtraction or division.