- Explain what algebra is for
- Distinguish expressions from equations
- Use the vocabulary: variable, coefficient, constant, term
Beyond arithmetic
In arithmetic you compute with known numbers: 3 + 4 = 7. In algebra you also work with unknowns — letters like x that stand for numbers you haven't found yet. That one idea unlocks equations, formulae and functions: the machinery of almost all higher mathematics.
Algebra is the branch of mathematics that uses letters to stand for numbers, and studies the rules for manipulating them.
Expressions vs equations
This distinction matters for everything that follows:
- An expression is a mathematical phrase:
3x + 2. No equals sign, no single answer — its value depends onx. - An equation is a mathematical sentence:
3x + 2 = 11. It claims two things are equal — and it can be solved.
Expression = phrase (3x + 2). Equation = sentence with = (3x + 2 = 11). Only equations have solutions.
The vocabulary
- Variable — a letter representing a number, e.g.
x. It can vary. - Coefficient — the number multiplying the variable: in
3x, the coefficient is 3. - Constant — a fixed number: in
3x + 2, the constant is 2. - Term — each part separated by
+or−:3x + 2has two terms.
Why letters?
Letters let you state general truths. a + b = b + a says addition works in any order, for any numbers — one short line replaces infinitely many examples like 3 + 4 = 4 + 3. Formulae like area = length × width are algebra: plug in numbers, get answers.
Practice
Coefficient 5, variable y, constant −7.
An equation — it contains = and can be solved for a.
Quick check
In the term 7x, what is 7?
Which of these is an equation?
How many terms does 2a + 3b − 5 have?
- Algebra uses letters to stand for unknown or general numbers.
- Expressions have no
=; equations do — and equations can be solved. - Know the vocabulary: variable, coefficient, constant, term.