Answer
Properties used are distributive, commutative, associative and commutative respectively.
Work Step by Step
Consider the expression and evaluate it:
\[7+2\left( x+9 \right)=7+\left( 2x+18 \right)\ \ \ (why?)\]
\[2\]is distributed over\[x\]and\[9\]. Thus, distributive property is used.
\[\begin{align}
& 7+2\left( x+9 \right)=7+\left( 2x+18 \right)\ \ \ (\text{distributive property}) \\
& =7+\left( 18+2x \right)\ \ \ (why?)
\end{align}\]
Order of addition is changed in \[\left( 2x+18 \right)\]. Thus, commutative property of addition is used.
\[\begin{align}
& 7+2\left( x+9 \right)=7+\left( 2x+18 \right)\ \ \ (\text{distributive property}) \\
& =7+\left( 18+2x \right)\ \ \ (commutative\ property) \\
& =\left( 7+18 \right)+2x\ \ \ (why?)
\end{align}\]
Associative property of addition is used as \[\left( 7+18 \right)\]is added first.
\[\begin{align}
& \left( 7+18 \right)+2x=25+2x \\
& =2x+25\ \ \ (why?)
\end{align}\]
Order of addition is changed in \[25+2x\]. Thus, commutative property of addition is used.
Hence, the properties used are distributive, commutative, associative and commutative respectively.
