Question

the expression (7+6v)+4v is simplified in several steps below. for each step, choose the reason that best justifies it. step reason (7+6v)+4v given expression 7+(6v+4v) select 7+10v select 10v+7 select

Explanation:

Step1: Identify the first step's property

The step \((7 + 6v)+4v\) to \(7+(6v + 4v)\) is using the Associative Property of Addition, which states that \((a + b)+c=a+(b + c)\) for real numbers \(a\), \(b\), and \(c\). So the reason for this step is the Associative Property of Addition.

Step2: Identify the second step's property

The step \(7+(6v + 4v)\) to \(7 + 10v\) is combining like terms. Since \(6v\) and \(4v\) are like terms (they have the same variable part), we add their coefficients: \(6+4 = 10\), so \(6v+4v = 10v\). The reason here is Combining Like Terms.

Step3: Identify the third step's property

The step \(7 + 10v\) to \(10v+7\) is using the Commutative Property of Addition, which states that \(a + b=b + a\) for real numbers \(a\) and \(b\). So the reason for this step is the Commutative Property of Addition.

Answer:

• For \(7+(6v + 4v)\): Associative Property of Addition
• For \(7 + 10v\): Combining Like Terms
• For \(10v+7\): Commutative Property of Addition