What is an equation?

An equation with an unknown

An equation is a mathematical equality that contains an unknown letter, usually denoted by x. For example:

3x + 5 = 14

This mathematical statement means: ‘if I multiply a certain number by 3 and then add 5, I get 14’. The aim is to find that number.

Key vocabulary

• The left-hand side: what is written before the = sign
• The right-hand side: what is written after the = sign
• The unknown: the letter whose value we are looking for (x, y, a...)
• The solution: the value of the unknown that makes the equation true

Solving means checking

Solving an equation means finding the value of x that makes both sides equal. For the equation 3x + 5 = 14, the solution is x = 3, because:

3 × 3 + 5 = 9 + 5 = 14. Both sides are indeed equal.

Why ‘first degree’?

An equation is said to be of the first degree when the unknown appears only raised to the power of 1 (never x², never under a root sign, never in the denominator).

Equation	First degree?
2x + 1 = 7	Yes
x² - 4 = 0	No (x squared)
5x - 3 = 2x + 6	Yes
1/x = 4	No (x in the denominator)

These first-degree equations are the simplest and most useful in everyday life: calculating prices, speeds, fair divisions, etc.