## 1. Introduction

This resource offers a simple explanation of how equations work, and how to rearrange and solve them.

An equation represents the equivalence between two quantities. The two sides of the equation are in balance, and solving equations involves maintaining the balance whilst rearranging different parts of the equation.

Equations are used to demonstrate relationships. A very simple example is:

2 + 5 = 7

So long as the same thing is done to both sides, the equation remains in balance. So if you subtract 2 from both sides:

2 + 5 - 2 = 7 - 2

5 + (2 - 2) = 7 - 2

5 = 5

Now replace one of the numbers with an unknown, represented by the symbol x:

x + 5 = 7

To find the value of x, you need to rearrange the equation so that the unknown (x) is on one side of the 'equals' sign, and everything else is on the opposite side. In this case, subtracting 5 from each side of the equation will leave the x on its own:

x + 5 - 5 = 7 - 5

x + 0 = 2