The idea
A variable is a name for a number: unknown for now, or allowed to change. The letter is a label so you can write one rule instead of many separate arithmetic copies.
Why it matters
Same structure, different numbers: a recipe scales, a budget has fixed and unknown lines, a distance problem ties rate and time. One expression with a variable covers all those instances.
How it works
In “x + 3,” x is either a chosen value or the single value that makes the sentence true after you add 3. Putting a number in place of x is substitution.
Example
“A ticket costs x dollars; two tickets cost 2x.” If x is 12, then 2x = 24. You did not need the price to write the relationship.
Try a number
Common mistakes
- Using the same letter for two different things in one problem.
- Dropping the variable mid-problem and guessing from memory.
Use the calculator
FAQ
- Can any letter be a variable?
Yes. Pick one meaning per problem and stick to it.
- What's next?
Solving equations shows how to isolate the variable and get a numerical answer.