Originally Posted by Dr. Fish

You know the distributive property, right? That means whenever you have something like:

x(y+z)

You can multiply the number outside the parentheses by each term in the parentheses, resulting in:

xy + xz

We will use that here, so:

n-(5n+2)=3(n-1)

Is the same thing as:

n-1(5n+2)=3(n-1)

...right? So you just take -1 times each term in the first parentheses and 3 times each term in the second parentheses, resulting in:

n-5n-2=3n-3

Then you just combine like terms and get the n variable to one side, then divide out the multiplier:

-4n-2=3n-3

-4n-2-3n+2=3n-3-3n+2

-7n=-1

n=1/7

Originally Posted by Snafu

The trick is to get all the variables on one side and get an x=# to find the solution. Also, a term like -(something+something) is exactly the same as (-1)(something+something), so you can distribute the negative sign just like you would any other number.

Lets come up with a similar problem, but with different terms for an example. Oh, say...

3x-(4x+3)=2(x-4)

First, let's distribute the 2 on the right side of the equals sign. This means we will multiply the 2 on the outside of the parentheses to all terms on the inside. Doing this should get you...

3x-(4x+3)=2(x)+2(-4)
3x-(4x+3)=2x-8

Move the 2x term to the other side of the equals by subtracting it on both sides like so...

3x-(4x+3)-2x=2x-2x-8
3x-(4x+3)-2x=-8

From here we find two like terms on the left side of the equals sign, 3x and -2x. Let's combine the terms 3x and -2x with simple math, leaving us with...

x-(4x+3)=-8

Remember the distribution thing I mentioned in the first paragraph? We apply this to the terms in parentheses and get...

x+(-1)(4x)+(-1)(3)=-8
x-4x-3=-8

Subtract -3 from both sides and combine like terms x and -4x, like we have done before to get...

-3x=-5

But we're still not done. Since we want to know what n is equal to, we have to get rid of that -3 in front of it. We can divide both sides by -3 to get 1x on the right side, leaving us with our desired lone x term. And thus...

-3x/-3=-5/-3

The -3's cancel on the left, and we end up with...

x=5/3

We're done!

If any of these examples leave you confused, (or if, God forbid, I made a mistake), lemme know. I might not be around to answer and of these questions, but I'm sure someone else will be willing to help you out.

EDIT: DAMNIT DR. FISH, YOU STOLE MY THUNDER. D:<