Math-y stuff

[Cosmic Fury]

IF YOU WANT TO POST BIG ALGORITHMS, LEAVE.

Anywho. So, this is pretty basic, but I have a question.

y-x=x-y

This isn't always true, but my teacher taught us that, if you want to get a number to the other side, for positives, you subtract that number from both sides (y/-y). For negatives, add. So, according to him, this should be possible, but if you substitute in, say x=5 y=6,

6-5=5-6

Unfortunately, 6-5=1 and 5-6=(-1).

Can anyone explain this to me?

If they both equal zero, they will be equal.

0-0=0-0

0=0

If they both equal 1, they will be equal this way as well.

1-1=1-1

0=0

Same goes if they both equal 2, 3, 4, and so on. If both variables are equal, they cancel each other out.



Problem solved.



========================

If you weren't after solving that equation, but figuring out how such equations work, then your teacher is pretty much right.

There is one rule you absolutely MUST follow: what you do to one side of the equation, you MUST do to another. Using that rule, let's solve a test equation:


X + 7 = 3X - 15

To solve this, you must isolate X by only having it on the opposite side of the equation as the constant. (The constant is number X equals.)

First, we must get the numbers on one side of the equation. We'll add 15 to both sides of the equation, to isolate the numbers on the left side.

X + 7 = 3X - 15

X + 7 + 15 = 3X - 15 + 15

X + 22 = 3X + 0

(The zero is there for convenience)

Now, we'll isolate X by subtracting 1X (or just X) from both sides of the equation.

X - X + 22 = 3X - X

22 = 2X

We still need to isolate X, because the equation only equals 2x, not 1x. We need to divide the equation by 2.

22----2x
----=-----
.2----- 2

11 = x


x = 11