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

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

Answer 1

To identify the properties that justify the steps between the lines you provided, we can analyze each step:

Line 1 to Line 2:

• The property that justifies the transition from Line 1 to Line 2 is the Commutative Property of Addition. This property states that the order in which we add numbers does not change the sum. In this case, the expression inside the parentheses moves from $4+7x$ to $7x+4$.

Line 2 to Line 3:

• The property that justifies the transition from Line 2 to Line 3 is the Distributive Property. This property states that $a(b+c)=ab+ac$. Here, $5$ is distributed to both $7x$ and $4$ in Line 2, resulting in $35x+20$.

So, the properties are:

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