Question 734479: How do I solve the following equation?
n + 2 / 5 = n - 14
My original problem was a word problem that stated:
2 more than a number divided by 5 is equal to 14 less than that number.
The answer I was given was 20, but that doesn't fit to balance the scales and I've found that the book sometimes has the wrong answers. If I use 18, I get 4 on both sides as the answer. If that's right, I don't know how to show my work. I found it just by using the 20 in place of the "n" and realizing that didn't work, so I started working backwards from there. I tried using the formulas I knew to figure it with the 20 as shown below and wasn't getting anywhere. I still can't make them work with the 18 either.
I've tried splitting the numerator, which gives me n/5 + 2/5, which I think is 2n/5 = n-14 because the denominators are the same, so I just add the top; then, multiplying by 5 on both sides, I end up with 2n = negative 70; when I minus the one "n" from the 2n, I get n= negative 70 which doesn't fit.
I also tried rearranging it like: n/5 + 2 = n - 14. In this case, I either get the same answer or I tried taking away the 2 on both sides first. Then, multiplying by 5 on both, giving me n = n-80. That doesn't make sense either.
Answer by ankor@dixie-net.com(22740)   (Show Source):
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