Question 758394: A student was told that in order to check a solution to a word problem like the one in problem 6, it is not enough to check that the solution she found satisfies the equation she set up, but rather that it is necessary to check the answer against the original problem. She would like to know why. How do you respond?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623)   (Show Source):
You can put this solution on YOUR website! Those two descriptions seem to be the same thing. Give us more information about the solution she set up. Was this after solving an analyzed set of equations, or was this solution set up directly from the analyzed worded description of the problem?
Sometimes, through the solution symbolic steps (arithmetic or algebra), multiplications or divisions create "extraneous" solutions as a result of the near-end of the process, and one or the other or so of these solutions will either NOT work in the original equation; or will make no sense for the original problem description.
You can or should try this help request again BUT TELL US EXACTLY What is "problem 6".
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website!
A student was told that in order to check a solution to a word problem like the one in problem 6, it is not enough to check that the solution she found satisfies the equation she set up, but rather that it is necessary to check the answer against the original problem. She would like to know why. How do you respond?
In most cases, the solution will satisfy the equation that is set up. However, if the equation that one sets up is not the correct one, it's likely that while that solution may satisfy the "set up" equation, it may NOT satisfy the clues that are given in the original problem. This is why it's imperative to check the solution against the ORIGINAL problem.
On the other hand, there are times when the problem is misinterpreted and so, an INCORRECT equation is set up. When checking the solution against the problem, the same error can be made in misinterpreting and/or misrepresenting the problem in the form of an equation and the solution therefore seem correct when in fact it's not.
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