Solving an equation

The first-degree equation

An equation is an equality to be found. To solve it is to determine the value of the letter that makes the equality true.

2x + 6 = 14

Here, only one value of x is correct. The aim is to make it appear on its own on one side of the equals sign.

The rule of the balance

An equation is a set of scales in balance. As long as you do the same thing on both sides, the balance is maintained.

2x + 6 = 14
2x + 6 - 6 = 14 - 6      (We remove 6 from both sides)
2x = 8
2x : 2 = 8 : 2           (we divide by 2 on both sides)
x = 4

There is no other principle to remember. Everything else follows from this.

That’s the advantage of equations: you can always check your result. Replace x with the value found in the original equation:

2 x 4 + 6  =  8 + 6  =  14   ✔

If you end up with something else, there’s a mistake somewhere. This habit of checking is better than any amount of proofreading.

Same method: group the letters on one side, the numbers on the other.

5x - 3 = 2x + 9
5x - 2x = 9 + 3          (the x's on the left, the numbers on the right)
3x = 12
x = 4

When a term ‘changes sides’, it changes sign. This isn’t an extra rule: it’s a shortcut for ‘I remove the same thing from both sides’.