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The basic idea is that you need to carry out the same operations on both sides of an equation.

In a scale, assuming you want to keep it balanced, if you add 3 kg. on the left side, you also need to add 3 kg. on the right side.

With an equation, the situation is similar; except that you can not only add and take away (add and subtract), but also (with certain limitations and caveats which you should learn) multiply both sides by the same number or term, divide both sides, square, take square roots, take trigonometric and inverse trigonometric functions, etc.

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Q: Why is a scale used often when explaining how to solve equations?
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