Understanding Variables

A variable is a letter or symbol that represents a number we don't know yet.

Common Variable Names

We typically use:

• $x$ - the most common variable
• $y$ - often used with $x$ in coordinate geometry
• $a$, $b$, $c$ - coefficients (numbers multiplied by variables)
• $n$ - often represents a count or whole number

Variables in Action

Example 1: Age Problem

"Sarah is 5 years older than her brother."

Let $x$ = brother's age Then Sarah's age = $x + 5$

If brother is 10: Sarah is $10 + 5 = 15$ If brother is 8: Sarah is $8 + 5 = 13$

Example 2: Perimeter of a Square

A square has 4 equal sides.

Let $s$ = length of one side Perimeter = $4s$

If $s = 5$: Perimeter = $4(5) = 20$

Key Terms

Term	Definition	Example
Variable	Letter representing an unknown	$x$ in $x + 3$
Coefficient	Number multiplied by a variable	$5$ in $5x$
Constant	A number without a variable	$7$ in $x + 7$

Practice Thinking

When you see $3x + 2$, think:

• "3 times some number, plus 2"
• $x$ could be any number
• The expression gives a rule that works for all values