Variable

Two different jobs

The same symbol does two quite different things, and mixing them up causes real confusion.

An unknown to find. In $x + 3 = 10$ there is exactly one number that works. Here $x$ is a specific value you have not identified yet, and solving means identifying it.

A quantity that varies. In $A = lw$, the letters stand for measurements that change from one rectangle to the next. Nothing is being solved; the formula describes a relationship.

Which job a letter is doing depends on the question, not on the letter itself.

Any letter works

$x$ is conventional but carries no special meaning. These say the same thing:

$$x + 3 = 10 \qquad n + 3 = 10 \qquad \square + 3 = 10$$

Formulas usually pick letters that hint at meaning — $t$ for time, $r$ for rate, $A$ for area — which makes them easier to read.

Why letters instead of a blank

A blank works for one unknown. Letters let you write two different unknowns in the same sentence and keep them apart, which is what makes literal equations and systems of equations possible.