variable expression

A variable expression is a phrase in the language of algebra that includes at least one letter standing for an unknown or changeable number. Where a numerical expression like 3 + 4 names a single fixed value, a variable expression like 3 + x names a value that depends on what x turns out to be.

It is built from variables and numbers joined by operations — addition, subtraction, multiplication, division, powers — such as 2x - 5, x^2 + y, or 4/(a + 1). Importantly, an expression is not an equation: there is no equals sign and nothing to “solve.” You can simplify it or evaluate it for chosen inputs, but on its own it just represents a quantity.

Because it contains a variable, a variable expression has no single value until you supply one. Substituting a number for the variable collapses it to an ordinary number; until then, it is a general stand-in for a whole family of values.