What Is a Variable?
A variable is a letter that represents an unknown or changing quantity. In algebra, x, y, and n are common choices. An expression combines variables, numbers, and operations — for example: 3x + 2.
Unlike an equation, an expression has no equal sign. You can't "solve" it, but you can evaluate it for specific values or simplify it.
Evaluating Expressions
To evaluate, substitute the given value and follow order of operations (PEMDAS):
- Evaluate 3x + 2 when x = 5: 3(5) + 2 = 15 + 2 = 17
- Evaluate 2x² − 5x + 1 when x = 3: 2(9) − 15 + 1 = 18 − 15 + 1 = 4
Like Terms and Simplification
Like terms have the same variable raised to the same power. You can add or subtract like terms:
- 5x + 3x = 8x (both are x-terms)
- 7x² − 2x² + 4x = 5x² + 4x
- 3x + 4 + 2x − 1 = 5x + 3
Constants (plain numbers) are like terms with each other. Terms with x² are only like terms with other x² terms.