###### Exercise52

A student has (correctly) simplified an algebraic expression in the following steps. Between each pair of steps, identify the algebraic property that justifies moving from one step to the next.

\begin{equation*} \phantom{={}}{6\!\left(c+8\right)+7c} \end{equation*}

• commutative property of addition

• commutative property of multiplication

• associative property of addition

• associative property of multiplication

• distributive property

\begin{equation*} ={\left(6c+48\right)+7c} \end{equation*}

• commutative property of addition

• commutative property of multiplication

• associative property of addition

• associative property of multiplication

• distributive property

\begin{equation*} ={\left(48+6c\right)+7c} \end{equation*}

• commutative property of addition

• commutative property of multiplication

• associative property of addition

• associative property of multiplication

• distributive property

\begin{equation*} ={48+\left(6c+7c\right)} \end{equation*}

• commutative property of addition

• commutative property of multiplication

• associative property of addition

• associative property of multiplication

• distributive property

\begin{equation*} ={48+\left(6+7\right)c} \end{equation*}
\begin{equation*} ={48+13c} \end{equation*}

• commutative property of addition

• commutative property of multiplication

• associative property of addition

• associative property of multiplication

• distributive property

\begin{equation*} ={13c+48} \end{equation*}
in-context