Question

Model each pair of algebraic expression using the key which of the following are not equivalent expressions A 2 ( x - 1 ) + y and 2x + y - 2 B x + 3 + 3y and X + 3 ( 1 + y ) C x + 4 + y + 4x + y D x + 4 + y and x + 5 + y - 1

Answer 1

To determine which pairs of algebraic expressions are not equivalent, we will simplify each expression and then compare them.

**A.** \( 2(x - 1) + y \) and \( 2x + y - 2 \)

1. Simplifying \( 2(x - 1) + y \):
\[
2(x - 1) + y = 2x - 2 + y = 2x + y - 2
\]

The two expressions are equivalent.

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**B.** \( x + 3 + 3y \) and \( x + 3(1 + y) \)

1. Simplifying \( x + 3(1 + y) \):
\[
x + 3(1 + y) = x + 3 + 3y
\]

These expressions are equivalent.

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**C.** \( x + 4 + y + 4x + y \)

1. Combining like terms:
\[
x + 4 + y + 4x + y = (x + 4x) + (y + y) + 4 = 5x + 2y + 4
\]

There is no second expression to compare in this pair.

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**D.** \( x + 4 + y \) and \( x + 5 + y - 1 \)

1. Simplifying \( x + 5 + y - 1 \):
\[
x + 5 + y - 1 = x + 4 + y
\]

These expressions are equivalent.

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Thus, the only pair of expressions from the list that can be said to contain a non-equivalent option based on your input is C, as it does not have a second expression to compare against.

However, all pairs A, B, and D are equivalent. Since we only identified one pair where no second expression exists, **none of the pairs A, B, and D provided are non-equivalent expressions.** Pair C is also equivalent by itself.

To summarize:
- **All pairs including functions A, B, C, D marked are equivalent wherein C stands alone.**