Variables, substitution and equivalent expressions

Strengthen the symbolic language needed throughout precalculus. This set distinguishes expressions from equations, explains coefficients and multiplication notation, and develops careful substitution into grouped expressions. It then moves to like terms, distribution, negative signs and equivalent forms, with each task designed to preserve the meaning of the original expression.

Practice begins with recognizing structure and evaluating given values. Later questions ask you to interpret a cost model, express a rectangle perimeter in different forms, diagnose an incorrect simplification and decide whether agreement at one input proves an identity. Single-answer and select-all questions encourage both calculation and checking every claim.

Use parentheses when replacing a variable with a negative number or with another expression. Combine only terms with matching variable parts, and justify equivalence with a property or a valid transformation rather than one successful numerical test. The explanations show how to do this and provide counterexamples where appropriate. Signed arithmetic and fraction operations are prerequisites. Formal equation solving comes later; this set focuses on interpreting and rewriting quantities, preparing you for exponent rules and subsequent algebraic models.