Question

2. Which pairs of expressions below are equivalent? (Select all that apply) A. x + y + x + y and 2(x + y) B. 5x + 3x – 2y and -2y + 8x C. 5(2x – 3y) and 10x – 3y D. 4x - 5y and 5y - 4x E. 6x – 8y and 3(2x - 4y) F. 9x + 2y and 11xy

Answer 1

A. Equivalent

B. Equivalent

C. Not equivalent

D. Not equivalent

E. Not equivalent

F. Not equivalent

Explanation:

A.

`\begin{gathered} x+y+x+y=2(x+y) \\ 2x+2y=2(x+y) \\ 2(x+y)=2(x+y) \end{gathered}`

The pair is equivalent

B.

`\begin{gathered} 5x+3x-2y=-2y+8x \\ -2y+8x=-2y+8x \end{gathered}`

The pair is equivalent

C.

`\begin{gathered} 5(2x-3y)=10x-3y \\ 10x-15y=10x-3y \\ 10x-15y\\e10x-3y \end{gathered}`

The pair is not equivalent

D.

`\begin{gathered} 4x-5y=5y-4x \\ 4x-5y\\e5y-4x \end{gathered}`

The pair is not equivalent

E.

`\begin{gathered} 6x-8y=3(2x-4y) \\ 3(2x-(8)/(3)y)=3(2x-4y) \\ 3(2x-(8)/(3)y)\\e3(2x-4y) \end{gathered}`

The pair is not equivalent

F.

`\begin{gathered} 9x+2y=11xy \\ 9x+2y\\e11xy \end{gathered}`

The pair is not equivalent