Suppose you were born on the same day as your neighbor, but she is 3 years older than you. When you were 1, she was 4. When you were 9, she was 12. When you are 42, she will be 45.

If we let $a$ represent your age at any time, your neighbor’s age can be expressed $a+3$.

your age	1	9	42	$a$
neighbor's age	4	12	45	$a+3$

We often use a variable, such as $x$ or $a$, as a placeholder for a number in expressions. Variables make it possible to write expressions that represent a calculation even when we don't know all the numbers in the calculation.

How old will you be when your neighbor is 32? We know your neighbor is 32. We also know your neighbor’s age is your age plus 3, or $a+3$. We can write the equation $a+3=32$ to represent these relationships. When your neighbor is 32 you will be 29, because $a+3=32$ is true when $a$ is 29.