Question

Which expression is an equivalent expression of 12x + 10 + 4y? Match the expressions with the property used to generate 5y + 2y + 6 + 2.

A) 12x + 4y + 10
B) 10 + 12x + 4y
C) 4y + 10 + 12x
D) 12x + 4y + 6 + 2

Answer 1

Options A, B, and C are equivalent expressions to 12x + 10 + 4y, using the commutative property of addition. The constants and variables have been rearranged, but they represent the same sum.

Step-by-step explanation:

The expression 12x + 10 + 4y can be rearranged to form an equivalent expression using the commutative property of addition, which states that the order in which numbers are added does not change their sum (A+B=B+A). This property allows for the rearrangement of the terms in an expression. Therefore, 12x + 4y + 10 (A), 10 + 12x + 4y (B), and 4y + 10 + 12x (C) are all equivalent expressions to 12x + 10 + 4y. The provided expression 5y + 2y + 6 + 2 can be seen as using the commutative property to rearrange and then combine like terms to get 7y + 8. However, option (D) 12x + 4y + 6 + 2 is not equivalent to the original expression because the constants 6 and 2 have not been combined.