Mathématiques

Expression, Equation, Identity

3x + 2 is an expression, 3x + 2 = 11 is an equation, 2(x + 1) ≡ 2x + 2 is an identity. What each one is, and what you are allowed to do to it.

Algebraic expression

An algebraic expression is a combination of numbers, variables and operations with no equals sign, such as 3x + 2.

Aussi appelé: Expression
Où les élèves le rencontrent: Grade 6 mathematics, where expression, equation and formula are first distinguished, and directly examined at GCSE and IGCSE, which also use the word identity and the ≡ sign.

La réponse en bref
An algebraic expression is a combination of numbers, letters and operations with no equals sign, such as 3x + 2. You can simplify, expand or substitute into an expression, but you cannot solve it. Add an equals sign and it becomes an equation, 3x + 2 = 11, which can be solved.

Un exemple

3x + 2 | 3x + 2 = 11 | 2(x + 1) ≡ 2x + 2

The first is an expression: it has a value once you choose x, and no value until you do. The second is an equation: it is true for x = 3 and false for everything else, which is what makes solving it meaningful. The third is an identity: both sides are the same expression written differently, so it is true whatever x is.

Three objects that look similar on the page

The equals sign is doing different work in each of these, which is why 'what is the answer' is a reasonable question for one of them and a meaningless one for another.

A formula is worth adding as a fourth. A = lw is an equation, but one that defines a quantity in terms of others and is used by substituting rather than by solving.

Expression — 3x + 2. No equals sign. It has a value only once x is given a value.
Equation — 3x + 2 = 11. A claim that is true for particular values of x, here just x = 3.
Identity — 2(x + 1) ≡ 2x + 2. True for every value of x; the ≡ sign says so.
Formula — A = lw. A relationship between quantities, used by substituting known values.

What you are allowed to do to each

With an expression you may rewrite it into an equivalent expression — expand it, factorise it, collect its like terms — and whatever you write must be equal to what you started with for every value of x. What you may not do is move something to 'the other side', because there is no other side. 3x + 2 does not become 3x = −2.

With an equation you may do the same thing to both sides, and that is exactly what solving is. The equals sign is the thing that makes the move legal, and it is missing from an expression by definition. This single distinction is behind a large share of algebra errors: a student who has been taught solving first tries to solve everything, including things that are not equations.

The parts of an expression

An expression is built from terms, separated by + and − signs. 3x + 2 has two terms; 5x² − x + 7 has three. Within a term, the pieces multiplied together are its factors: 3x has the factors 3 and x.

The number multiplying the variable is the coefficient, and a term with no variable is the constant. Questions use these names rather than pointing at the numbers, so 'write down the coefficient of x' and 'how many terms does this expression have' are both asking something precise.

Questions fréquentes

Can you solve an expression?

No, and a question will never ask you to. Solving means finding values that make a statement true, and an expression makes no statement — it is a number written in an incomplete form. Questions about expressions say simplify, expand, factorise or evaluate. The word 'solve' only follows an equals sign.

What is the difference between an expression and an equation?

The equals sign, and what it lets you do. An expression, 3x + 2, is a quantity. An equation, 3x + 2 = 11, is a claim that two quantities are equal, which you can act on by doing the same thing to both sides. One has a value; the other has a solution.

What does the ≡ sign mean?

It marks an identity — a statement true for every value of the letters, not just some. 2(x + 1) ≡ 2x + 2 holds whatever x is. Exam questions sometimes give an identity with unknown coefficients and ask you to find them, which works by comparing the numbers in front of matching powers on each side.

Is a formula an expression?

No, a formula is a kind of equation: it has an equals sign and a subject, like A = lw or v = u + at. The right-hand side of a formula is an expression. The difference in practice is that formulae are used by substituting numbers in, rather than by being solved.

Dernière mise à jour 21 août 2026