Question

Model each pair of algebraic expression using the key which of the following are not equivalent expressions answer A 2 ( x - 1 ) + y and 2x + y - 2 answer B x + 3 + 3y and X + 3 ( 1 + y ) answer C x + 4 + y + 4x + y answer 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 in the pairs given (A, B, C, D) and see if they are equal or not.

**Answer A:**
1. \(2(x - 1) + y\)
= \(2x - 2 + y\)
= \(2x + y - 2\)

**Conclusion:** Both expressions are equivalent.

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**Answer B:**
1. \(x + 3 + 3y\)
= \(x + 3y + 3\) (rearranged)

2. \(x + 3(1 + y)\)
= \(x + 3 + 3y\)

**Conclusion:** Both expressions are equivalent.

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**Answer C:**
1. \(x + 4 + y + 4x + y = 5x + 2y + 4\) (combine like terms)

**Conclusion:** The expression simplifies to \(5x + 2y + 4\).

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**Answer D:**
1. \(x + 4 + y\)
= \(x + y + 4\)

2. \(x + 5 + y - 1\)
= \(x + y + 4\)

**Conclusion:** Both expressions are equivalent.

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### Summary:
- **Answer A:** Equivalent
- **Answer B:** Equivalent
- **Answer C:** \(5x + 2y + 4\) (not directly compared, but can check for the other expressions)
- **Answer D:** Equivalent

The only pair that simplifies differently based on the task at hand is **Answer C** compared to the others, as the equivalent expression was not matched directly with another.

### Final Determination:
The answer pairs that are **not equivalent** are the ones that were not compared directly; thus, the answer is **C**: \(x + 4 + y + 4x + y\) does not match the simplified nature of others producing simpler forms.