# Algebra Introduction

### Topics

There’s more to making numbers negative than just putting a little line in front of them: you have to really *understand* what a negative number is and how to deal with one in unusual circumstances.

For example, is -(-(-(-(-5) negative or positive? Who knows? (You do.)

Clearly, the first negative sign—the one directly attached to the 5—makes the number negative. But the next sign reflects the number back across 0 on the Number Line, making it positive once again. After we make a few more flips and wait until the dust settles, we discover that this number is indeed negative, but you can’t make that assumption just because there are negative signs coming out your ears.

When you have a negative variable on one side of an equation that you want to move to the other side, you need to be able to recognize two things:

- Whether the number gets lonely and needs to be moved with any other terms, and
- Whether the move will
*negatively*affect your number. Get it? Negatively affect...oh, never mind.

Most of the examples in this guide are fairly straightforward, but things can get confusing pretty quickly. (Example one: quintuple negatives.) Take your time with negative numbers, and make sure you get what’s going on before you start slinging them around willy-nilly.