algebraic expression

An algebraic expression is a recipe for a calculation, written with numbers, variables, and operation signs — but with no equals sign. Think of it as a phrase, not a full sentence: “twice a number plus three,” or 2x + 3. It describes what to do, but it does not assert that anything is equal to anything.

Because it has no equals sign, you cannot “solve” an expression; there is nothing being claimed and so nothing to find. What you can do is simplify it (write it more compactly), expand it, factor it, or evaluate it once you know the values of its variables. An expression is a thing with a value, the way a noun phrase names a thing.

The contrast with an equation is the key idea. An expression like 2x + 3 is one side of a potential statement; an equation like 2x + 3 = 11 joins two expressions with an equals sign and so makes a claim that may be true for certain values of x. Mixing up these two — trying to “solve” an expression, or “simplifying” an equation as if it had no two sides — is one of the most common early confusions.