explain why a solution of a word problem should be checked using the original wording of the problem and not the equation written from the wording
When you check your answer with the original problem, you'll see whether your answer makes sense.
When solving a word problem, it is important to check the solution using the original wording of the problem rather than solely relying on the equation that you derived from it. This is because word problems often involve real-life scenarios and the language used to describe them can be nuanced and context-dependent. By reviewing the original wording, you ensure that the solution aligns with the problem's intended meaning and accurately addresses the question being asked.
Here are a few reasons why checking the solution against the original wording is crucial:
1. Clarifying the problem's intent: The original wording provides essential context that may help clarify the specific elements or conditions involved in the problem. It may mention certain constraints or limitations that are not explicitly stated in the equation. By referring back to the wording, you can ensure that your solution adheres to these constraints and accurately reflects the problem's intent.
2. Identifying possible errors or oversights: By verifying the solution against the original wording, you can catch any mistakes you may have made during the problem-solving process. It is possible to make errors when translating the language of the problem into an equation, which could lead to an incorrect solution. Checking against the wording allows you to detect any discrepancies or oversights and correct them accordingly.
3. Integration of relevant units and dimensions: Word problems often involve measurements, units, or dimensions that are integral to the problem's formulation. The process of converting the wording into an equation might require you to algebraically manipulate these units or dimensions. Verifying the solution against the original wording helps ensure that any conversions or unit manipulations were accurately performed, allowing you to confirm that the final solution is in the correct units and dimensions.
4. Investigating extraneous solutions: Sometimes, during the process of solving the equation, you might obtain extra solutions that do not fit the original problem's context. By referring to the original wording, you can identify and discard these extraneous solutions, or reevaluate your equation if necessary. This step helps you avoid misinterpreting the problem or considering irrelevant solutions.
In summary, checking the solution against the original wording of a word problem is essential to confirm its accuracy, address any contextual considerations, and validate that it effectively resolves the question asked. This comprehensive approach promotes a deeper understanding of the problem and increases the likelihood of obtaining the correct solution.