Distinguish expressions, equations and identities

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Distinguish expressions, equations and identities

An expression names a value through numbers, variables and operations. An equation states that two expressions are equal and may hold only for particular inputs. A formula expresses a relationship between quantities, often using an equation.

An identity is true for every allowed input, such as 2(x+3) ≡ 2x+6. An inequality compares sizes rather than asserting equality. The allowed domain still matters: expressions containing division cannot use a denominator of zero.

Terms are separated by addition or subtraction at the relevant top level; factors are multiplied. In 3x+2, the terms are 3x and 2, while 3 and x are factors of the first term. In 3(x+2), the bracket is one whole factor.

Worked example: Classify 3x+2, 3x+2=14 and 2(x+3)≡2x+6.

The first gives a value without a relational sign.

The second is an equation satisfied by x=4.

The third is an identity explained by distribution.

Answer: Expression; equation; identity.

Check your understanding: Are x+2 and x×2 the same kind of combination?

Answer: No: one is a sum; the other is a product.

Why: Terms in a sum and factors in a product support different manipulation rules.