To determine whether the two algebraic models represent equivalent expressions, you need to analyze each model and how they relate to each other based on the properties of algebraic expressions.
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Equivalent Expression Definition: Two expressions are equivalent if they yield the same value for the same variable(s), or if they can be transformed into one another through the addition or removal of opposite pairs.
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Model Analysis:
- If Model 1 can be simplified by removing opposite pairs to arrive at Model 2, or vice versa, then the expressions are equivalent.
- Likewise, if you can show that adding or removing terms in either model can lead to the same expression/result, then they are also considered equivalent.
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Evaluating Given Responses:
- If Model 1 can be simplified by removing opposite pairs to get Model 2, this suggests that they are equivalent.
- The third and fourth options about adding opposite pairs could indicate that they lead to different expressions, which would mean they're not equivalent.
- The last option seems to suggest that Model 2 remains unchanged when opposite pairs are added, which could indicate equivalence.
Given this reasoning, if we know that removing pairs in one model leads to the other model, then we can confidently say those models are equivalent. The best response appears to be:
Yes; Removing opposite pairs in Model 1 creates Model 2.
Based on the provided responses, please choose the most fitting according to your analysis of the specific models in question.
1 answer