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o far we’ve been dealing with relatively simple situations that only require a little thought to work out which calculations you need to do to get the answer. From now on, we’ll be dealing with situations in which working out what to do is much more difficult.

Elementary algebra gives us a way around this: equation solving. Instead of having to keep track of a bunch of different quantities and figure out which calculations to make with them, algebra lets you manipulate symbols for the numbers according to certain rules.

It will take you a while to get used to this, and the rules can be hard to remember at first, but elementary algebra is something you will need to know to study anything but the simplest mathematics or science. The rest of this book requires it.

Most algebra textbooks simply tell you the rules without any explanation, and recommend mnemonics to memorise them. We will be deriving them from the properties that we’ve discovered in previous chapters. Instead of learning procedures that only work for certain situations, you will learn general skills and use your own ingenuity to solve problems.

If you’ve completed Chapter 3: Adding and Subtracting, Chapter 4: Multiplying and Dividing, and Chapter 5: Exponents and Logarithms, you should be ready for this one. You don’t necessarily need to have good arithmetical skills, but you need to understand what addition, multplication, and so on mean, and in what situations they apply.