Exercise43

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.

\(\phantom{={}}{2\!\left(x+9\right)+5x}\)

?

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={\left(2x+18\right)+5x}\)

?

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={\left(18+2x\right)+5x}\)

?

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={18+\left(2x+5x\right)}\)

?

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={18+\left(2+5\right)x}\)

\(={18+7x}\)

?

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={7x+18}\)

in-context