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Linear equations
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Equations

This is where many people stall in their mathematical progress. This is often down to the problem of Mt Stupid in the Dunning-Kruger graph. Or in other words a refusal to take advice on the approach to take. Please don't make this error, as have so many before you.

Equations are very simple to start with and it is this which can give the unwary an unexpected confidence boost, at just the wrong time. So take your time and think about each step before you commit to it.

An equation is a balance. It sounds obvious but if 2 expressions has an equals sign $=$ between them, this tells us that they are, despite looking a bit different, are, in fact, exactly the same.

As with most of the topics covered here, the best way to get ahead is to go through the worked examples. Work them through yourself. If you just read what I have written, it will go in one eyeball and straight out through the other one. A waste of time. Really...a complete waste of time. Maths is as much a doing thing as music or sport. In order to understand the dots in music, you have to have some way of turning those dots into sounds. In sport, to acquire a skill, you have to practise it; theory will only get you so far. Mathematics is much the same; you have to do it, to get good at it.

The Golden Rule of Equations

There is only one thing you need to hold in your mind when you are solving equations, and it is this:

Whatever you do to one side of an equation, you must do the exact same thing to the other side of the equation as well.

It really is that simple. If that is how you think about the problem, you will not go wrong.