Math Stuff.

quote: because (somehow) the 5 is negitive, even though it looks like subtraction

Wat? They're the same thing. x - y is equal to x + (-y)

The rule is 'subtracting by a positive number is the same as adding a negative number'. Thus it should be:
4 - 45x - 40x

which can be simplified to:
4 - 85x

since the two latter terms are both multiplied by x.

quote: Because teacher told me to multiply by negitive to simplify, but I think 4 - 5 is subtraction, not a negiitive 5

Don't forget about the invisible multiplication symbol:

4 - 5 * (9x + 8x)

Remember that multiplications and divisions are done before additions and subtractions. As such you multiply 17x by -5.

Well actually, you don't really have to multiply by -5. You can also just multiply by 5..

4 -5(9x + 8x) =
4 - (45x + 40x) =
4 - (85x) =
4 - 85x

or alternatively..

4 -5(9x + 8x) =
4 - (45x + 40x) =
4 - 45x - 40x =
4 - 85x

or alternatively..

4 -5(9x + 8x) =
4 -5(17x) =
4 - (85x) =
4 - 85x

quote: Skasi x + (-y)

quote: fxrs In addition to what others pointed out

Kden.

Parzival why don't you write a "widget" that solves these problems? That would be a lot easier than the train factory and assures you understood how to solve the problem in general. (Also that's how I avoided boring math homework at school :P)

If i inferred correctly that you're not yet going to university you might wanna have a look at the USACO. It's a programming contest that yearly sends a team of 4 students to the IOI (next year in Iran, last years were Russia, Kazakhstan, Taiwan, Australia). IMO it's the best way to learn programming while also getting to travel the world for free ;)

Btw, why is this in General Discussion?

(All of this has probably been said above in one form or another, but I'll try to make it really really explicit.)

quote: However, teacher tells me I am wrong after I solve because (somehow) the 5 is negitive, even though it looks like subtraction. Is there any rule in algebra that says it is negitive instead of subtraction, and if there is how could I tell signs apart?

The negative sign works the same as subtraction, so there is no need to distinguish between them.

In this case, the mistake you've made is not being careful about what you're subtracting.

If you remember your order of operations brackets comes before multiplication comes before addition and subtraction.

4 - 5(9x + 8x)

The trick here is that we are subtracting the entire 5(9x+8x) term, not just the 5 and not just the 5 * 9x term.

Evaluating the brackets first gives

4 - 5 * 17x

then multiplying gives

4 - 85x

then we would subtract, but we can't simplify this expression any further.

This is the most direct way to simplify the expression. There are other sequences of legal rearrangements, all of which give the same solution:

(1) we can multiply before evaluating the brackets, as long as we multiply the entire expression that is within the brackets.
4 - 5(9x + 8x)
4 - (5*9x + 5*8x)
4 - (45x + 40x)
4 - 85x

(2) we can turn the subtraction into an addition by using the rule "a - b = a + (-b)". Observe that we need to use the same rule in reverse at the end. Things like that are very common in arithmetic.
4 - 5(9x + 8x)
4 + (-(5(9x + 8x)))
4 + ((-5)*(9x+8x))
4 + (-85x)
4 - 85x

bonus question: what is wrong with the following proof? (I know it's an old one... If you already know or work it out, don't spoil it for anybody else please :D )
[Spoiler]

[Spoiler]

We would need a basic logic thread to figure that out :P

Just... wow.