Variables & terms

A ticket costs 12 euros. What do 2 tickets cost? What about 5? Instead of writing a new calculation every time, you just say: 12 times the number of tickets. That is exactly what variables do: a letter stands for a number you don't know yet or that can change. You write a rule once and use it again and again.

Letters as placeholders

A variable is a placeholder for a number, usually written as x, y, or n. A term is an expression that may contain such placeholders, for example x + 4 or 3x. Important: 3x is short for 3 · x, the multiplication sign is simply left out. So the term 12n describes the ticket price from above: 12 euros times n tickets.

Substituting: giving the term a value

As long as x is unknown, a term like 3x + 2 is just a recipe for a calculation. As soon as you substitute a number for x, you can work it out: for x = 5, 3x + 2 becomes 3 · 5 + 2 = 17. This is called evaluating the term. Try plugging in different numbers, each value of x gives a different result. Terms may contain powers too: x² is short for x · x. When you evaluate, the usual order applies, first the power, then multiplication and addition. So for x = 4 you get x² = 4 · 4 = 16 and therefore 3x² = 3 · 16 = 48.

Combining like terms

2 apples plus 3 apples make 5 apples. In the same way, 2x + 3x = 5x. You can combine terms with the same variable by adding the numbers in front. An x with no number in front means 1, so x is the same as 1x and 4x + x combines to 5x. But be careful: 2x + 3y stays as it is, because you can't mix apples and pears. Likewise 2x + 3 can't be simplified further, the 3 has no x.