Question

Identify the property that justifies each step asked about in the answer area below.
Line 1: , 5, left parenthesis, 4, plus, 7, x, right parenthesis
Line 1: =
5(4+7x)
Line 2: , 5, left parenthesis, 7, x, plus, 4, right parenthesis
Line 2: =
5(7x+4)
Line 3: , 35, x, plus, 20
Line 3: =
35x+20

Answer 1

For each line of the expression, here are the steps identified along with the properties that justify each transformation:

**Line 1: \( 5(4 + 7x) \)**
- This line is the original expression, so there is no property needed to justify it.

**Line 2: \( 5(7x + 4) \)**
- **Property:** Commutative Property of Addition
- **Justification:** The expression inside the parentheses changes from \( (4 + 7x) \) to \( (7x + 4) \) by rearranging the order of the terms. The commutative property allows us to change the order of addition.

**Line 3: \( 35x + 20 \)**
- **Property:** Distributive Property
- **Justification:** The expression \( 5(7x + 4) \) is simplified by distributing the \( 5 \) across both terms inside the parentheses, giving us \( 5 \cdot 7x + 5 \cdot 4 \), which simplifies to \( 35x + 20 \).

Thus, the properties that justify each step are:

- **Line 2:** Commutative Property of Addition
- **Line 3:** Distributive Property