Question

Which of the following properties are being used to simplify the statement (3x + 4y) + 5x = 8x + 4y? Associative and commutative properties of addition Associative property of addition and commutative property of multiplication O O OC Associative and commutative properties of multiplication Associative property of multiplication and commutative property of addition

Answer 1

Associative and commutative properties of addition

Explanation:

The one thing that the associative property of addition says that

`(a+b)+y=a+b+y`

and the commutative property of addition says

`a+b=b+a`

(the order of addition does not matter )

Now, the steps we take to solve our equation are the following:

`\begin{gathered} \mleft(3x+4y\mright)+5x=8x+4y \\ 3x+4y+5x=8x+4y\text{ (the associative property of addition )} \end{gathered}`

The second step is

`\begin{gathered} 3x+4y+5x=8x+4y\text{ } \\ 3x+5x+4y=8x+4y\text{ (commutative property of addition.)} \end{gathered}`

which simplifies to

`\begin{gathered} 8x+4y=8x+4y \\ 4y=4y \end{gathered}`

Hence, we used associative and commutative properties of addition to solve our equation.