Lesson 6 of 16Article16 min
Algebra Begins: Variables & Expressions
A variable is a symbol (usually a letter) that stands for a number we do not yet know — or for any number in a family of cases. An expression combines numbers, variables, and operations; it does not assert equality.
01Letters as placeholders
A variable is a symbol (usually a letter) that stands for a number we do not yet know — or for any number in a family of cases. An expression combines numbers, variables, and operations; it does not assert equality.
- Term: a product like 3x, −7y², or a constant 5.
- Coefficient: the numeric factor of a term (in −7y² the coefficient is −7).
- Like terms share the same variable factors: 3x and −5x can combine; 3x and 3x² cannot.
- Simplify by combining like terms and using exponent laws.
02Evaluating expressions
To evaluate, substitute the given values and follow order of operations. Use parentheses when substituting negatives so signs stay clear.
Example: evaluate 2x² − 3x + 1 at x = −2 → 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15.