SOLUTION: My 4th grade son was given the equation 3x-9=70. The answer the teacher wanted was x=26.33333 (with a line over the last three to show that it repeats indefinitely). My question

Algebra ->  Equations -> SOLUTION: My 4th grade son was given the equation 3x-9=70. The answer the teacher wanted was x=26.33333 (with a line over the last three to show that it repeats indefinitely). My question       Log On


   

Question 356817: My 4th grade son was given the equation 3x-9=70. The answer the teacher wanted was x=26.33333 (with a line over the last three to show that it repeats indefinitely). My question is: how is this a valid equation? When you plug the value of x back in, you are never going to get 70, but something that is slightly less than 70 (69.99999.....). My son did get the answer she wanted, but it was my understanding that the whole point of finding the value of the variable was finding the value that makes the equation true. A second algebra teacher tells me that this is a completely valid question but couldn't explain why it is valid when it is untrue. If someone could explain to me how 69.99999 = 70, I would be very grateful!
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3x-9=70
3x=79
highlight%28x=79%2F3%29
.
.
.
That's the real answer.
It's unfortunate that some teachers nitpick over minor details and require answers in a certain format.
If the answer is not x=79%2F3 then it's an approximation.
Sometimes approximations are good enough.
Lines over repeating numbers are only used in algebra books and not in the real world.
Unfortunately its nonsense like this that stifles the creativity, wonder, and excitement that should go along with learning mathematics.
Hopefully, this experience won't dull your son's enthusiasm for algebra and learning in general.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If someone could explain to me how 69.99999 = 70, I would be very grateful!
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Let x = 69.999999 endlessly
----
Then 10x = 699.99999endlessly
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Subtract the 1st equation from the 2nd to get:
9x = 630
---
Divide by 9 to get:
x = 70
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Therefore x = 69.99999... = 70
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Fact: Every repeating decimal can be written as a/b
where a and b are integers and b is not zero.
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Cheers,
Stan H.