What makes an algebraic expression different from an equation?

Look for what the writing is saying. An expression represents a quantity; an equation states that two quantities are equal. An expression can be a number, a variable, or numbers and variables joined by operations. For example, 4n + 3 is an expression. An equation connects expressions with an equals sign, as in 4n + 3 = 19. [S1]

Comparison chart

• Expression: 4n + 3 — represents one quantity; it does not assert that the quantity equals something else.
• Equation: 4n + 3 = 19 — asserts that the quantity on the left equals 19.

The expressions on either side of an equation are its left-hand and right-hand sides. The equals sign is the key clue; a variable by itself doesn’t make something an equation.

Yes: x + 5 is still an expression on its own. The surrounding words may tell you what to do with it, but they don’t add an equals sign to the written expression. If a problem says, “The number plus 5 is 12,” you can translate that statement into the equation x + 5 = 12. The expression is x + 5; the full translated statement is an equation because it asserts equality.

Keep the written math separate from the task instruction. “Simplify x + 5” gives you an expression to work with. “Solve x + 5 = 12” gives you an equation to solve.

Yes. Each side of an equation can be an expression. For instance, 2(a + 1) = a + 7 has the expression 2(a + 1) on the left and a + 7 on the right. The equation says those two quantities are equal.

An equals sign identifies an equation, but it doesn’t by itself tell you the requested task. You might be asked to solve an equation, check whether a proposed value makes it true, or simply classify it. Follow the instruction in the problem. Classification and solving are different steps: first identify the kind of object, then decide what the prompt asks you to do.

Try each one before reading the answer key. Ask: does the written math assert that two quantities are equal?

1. 7p - 2
2. 7p - 2 = 12
3. m + 4 = 4 + m
4. 3(r - 1)
5. 8 = 2q

Answers: 1 is an expression; 2 is an equation; 3 is an equation; 4 is an expression; 5 is an equation. In 3, both sides are expressions, and the equals sign makes the whole statement an equation. In 5, a variable appears on only one side, but that doesn’t change the classification.

Reusable method: locate an equals sign, then check whether it asserts that the two sides are equal. If so, classify the whole item as an equation. If there is no equality statement, classify it as an expression. Then read the surrounding directions to find out whether you should simplify, evaluate, solve, or merely identify it. This method classifies the examples; it doesn’t determine whether an equation is true for every value or how to solve it.