Lesson 4: Variables & Expressions
Algebra begins with variables — letters that represent unknown or changing values. Expressions combine variables with numbers and operations. Learning to write, read, and evaluate expressions is the foundation of all algebra.
Key Concepts
Variables
A variable is a symbol (usually a letter) representing a number. x = 5 means x has the value 5. Variables let us write general rules. Area = length × width = l × w — this works for ANY rectangle.
Algebraic Expressions
An expression is a combination of numbers, variables, and operations. 3x + 7, 2a - b + 4, x²- 5x + 6. Expressions don't have an equals sign (that would make it an equation).
Evaluating Expressions
Substitute the value and calculate. If x = 3: 2x + 5 = 2(3) + 5 = 6 + 5 = 11. If a = 4, b = -2: a² - 3b = 16 - (-6) = 22.
Like Terms
Like terms have the same variable and exponent. 3x and 7x are like terms (combine to 10x). 3x and 3x² are NOT like terms. Combine like terms to simplify: 4x + 3y - x + 2y = 3x + 5y.
🔬 Interactive Lab: Variables & Expressions Lab
✅ Check Your Understanding
1. If x = 4, what is 3x - 7?
2. Which are like terms?
3. Simplify: 5x + 2y - 2x + y