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.
Letters 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.
Writing 2 × x as 2x is convention, not a new operation. Juxtaposition means multiplication.
Evaluating 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.