I hope you don't mind if I don't tell you the answer right away. But, if you're still having trouble I could tell you the answer and show you how I got it step by step.
Anywho, this problem can be solved two ways.
Option 1. Turn the fractions into decimals
In my opinion and experience, I think this is the easiest way to approach a problem like this when it has fractions. To change a fraction into a decimal you would have to divide the denominator by the numerator.
So let's take 1/4 for instance. Put the denominator, 4, in the inside of the tent (I don't know what you call the division thingy I call it a tent cause it looks like it) and put the 1, the numerator, on the outside. Since 4 can't go into 1, you have to put in a decimal point and write in a 0 so 1 becomes 1.0 and the top of the tent should have a decimal point too. Now you can divide 4 by 1(.)0 which will become 0.25. 3/2 can be turn in a decimal in a similar way.
After you turn the two fractions into decimals, you can solve this equation more easily. It doesn't matter whether you subtract 1.5n from 0.25n or visa versa. Just remember what you do to one side you have to do to the other. So if you subtract 1.5n from itself (1.5n-1.5n which cancels it out), you have to then do the same on the other side(1.5n-0.25n)
Now that you have only one n, the problem should be much easier to solve. Just solve for n and you'll get your answer. d=(´▽｀)=b
Option 2. Change one fraction's denominator then solve
This method I just discovered how to do. My teacher did teach a method how to actually solve equations with fractions without turning them into decimals, but that was WAY too confusing, so after solving this problem and thinking about it I found a much better way.
Change one of the fraction's denominator so it is the same as the other. Let's take 3/2n as it is quick and easy to do. The denominator for 3/2 has to be the same as 1/4n's denominator, 4.
Forget the n for a minute. You have multiply 3/2 with a fraction (always the numerator and denominator number are the same) that will turn the denominator from 2 to 4. I multiplied 3/2 by 2/2 and got 6/4 thus the denominator is now the same as the 1/4's denominator. Now plug the number back the equation with the n and it will become 1/4n+5=6/4n-10 . Now can solve this much easier.
Remember it doesn't matter if you subtract 1/4n from itself or 6/4n from itself just do the same on the the other side. I subtracted 1/4n from itself and then subtracted 1/4n from 6/4n. Next solve for n.
There is going to be a part where you have to divide a fraction by a fraction. Remember that in order to do that you have to switch the second fraction( so the numerator become the denominator and the denominator becomes the numerator) and multiply. For example (this is unrelated to the problem), (2/4)/(2/4). Flip the second fraction's denominator and numerator so it becomes 4/2. Multiply that by 2/4 and you'll get 8/8 which is basically 1.
Once you get past that part, you have the answer ≧ω≦
Hints to help you out:
*The answer is not a fraction
*DON'T forget to simply the final fraction (after you divide)
*Plug the answer for n back into the equation and solve. If both equations have the same answer then it your answer for n is right, if not you made a mistake
*Watch your signs and operations
*I kinda gave away the decimal version of 3/2 in my explanation
I hope this helps and I didn't complicate the explanation. Again if you still need help and just can't figure out the answer, message me and I'll show/tell you step by step of how I got the answer.
