Answer
Properties used are distributive, commutative, associative, distributive and commutative, respectively.
Work Step by Step
Consider the expression and evaluate it as,
\[5\left( x+4 \right)+3x=\left( 5x+20 \right)+3x\ \ \ (why?)\]
\[5\]is distributed over\[x\]and\[4\]. Thus, distributive property is used.
\[\begin{align}
& 5\left( x+4 \right)+3x=\left( 5x+20 \right)+3x\ \ \ (\text{distributive property}) \\
& =\left( 20+5x \right)+3x\ \ \ (why?)
\end{align}\]
Order of addition is changed in \[\left( 5x+20 \right)\]. Thus, commutative property of addition is used.
\[\begin{align}
& 5\left( x+4 \right)+3x=\left( 5x+20 \right)+3x\ \ \ (\text{distributive property}) \\
& =\left( 20+5x \right)+3x\ \ \ (commutative\ property) \\
& =20+\left( 5x+3x \right)\ \ \ (why?)
\end{align}\]
Associative property of addition is used as \[\left( 5x+3x \right)\] and is added first.
\[\begin{align}
& 20+\left( 5x+3x \right)=20+x\left( 5+3 \right)\ \ \ (why?) \\
& =20+8x
\end{align}\]
\[\left( 5+3 \right)\]is distributed over \[x\]. Thus, distributive property is used.
\[20+8x=8x+20\ \ \ (why?)\]
Order of addition is changed in \[\left( 20+8x \right)\]. Thus, the commutative property of addition is used.
Hence, properties used are distributive, commutative, associative, distributive and commutative respectively.
