Variables and Expressions
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn what a variable is, how to translate everyday situations into algebraic expressions, and how to evaluate an expression by plugging in a number. This is the foundation everything else in algebra builds on.
The Concept
Section titled “The Concept”A variable is a letter that stands in for a number we don’t know yet. We usually use letters like x, y, or n, but any letter works.
An algebraic expression combines numbers, variables, and operations. For example:
This means “take some number x, multiply it by 3, then add 5.” There’s no equals sign. It’s an expression, not an equation.
Some common vocabulary:
- Coefficient - the number in front of a variable. In , the coefficient is 3.
- Constant - a number on its own with no variable attached. In , the constant is 5.
- Term - a single piece of an expression separated by + or − signs. The expression has two terms: and .
To evaluate an expression, replace the variable with a specific number and compute the result. If :
Worked Examples
Section titled “Worked Examples”A streaming service charges a 10 dollar monthly base fee plus 3 dollars per movie you rent. Write an expression for the monthly cost, then find the cost if you rent 6 movies.
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Identify the variable. Let m = the number of movies rented.
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Write the expression.
The base fee is the constant (10), and represents 3 dollars times however many movies you rent.
- Evaluate for .
Your monthly cost would be 28 dollars.
Real-World Applications
Section titled “Real-World Applications”Algebraic expressions are everywhere once you start looking. Budgeting (“I spend x dollars on coffee each week”), fitness (“I burn calories where t is minutes of running”), and even cooking (“double the recipe” means multiplying every ingredient by 2) all use the same idea: a pattern with a slot you can fill in with different numbers.
Understanding expressions lets you set up problems before you solve them, which is the real power of algebra.