Question

Which pair of expressions are equivalent?

A.
2y – 4 and 2y – 4 + 9
B.
14x – 7 and 7x – 14
C.
9y + 3 + 2 and 3(y + 1) + 2
D.
x + y and x – y + 2y
E.
x + 2y and x – y

Answer 1

[AI-generated answer — Explain Bot]

To determine which pair of expressions are equivalent, let's analyze each option:

A. 2y – 4 and 2y – 4 + 9
These expressions are not equivalent because the second expression (2y – 4 + 9) can be simplified to 2y + 5.

B. 14x – 7 and 7x – 14
These expressions are not equivalent because the second expression (7x – 14) simplifies to 7(x – 2).

C. 9y + 3 + 2 and 3(y + 1) + 2
To simplify the first expression, we add 3 + 2 to get 5, so the expression becomes 9y + 5.
Simplifying the second expression, we distribute the 3 into the parentheses and then add 2: 3y + 3 + 2 = 3y + 5.
Therefore, these expressions are equivalent.

D. x + y and x – y + 2y
These expressions are not equivalent because the second expression (x – y + 2y) simplifies to x + y.

E. x + 2y and x – y
These expressions are not equivalent in general. However, if we have additional conditions or values assigned to x and y, they might be equivalent. Without more context, we cannot determine the equivalence.

In conclusion, the pair of expressions that are equivalent is:
C. 9y + 3 + 2 and 3(y + 1) + 2