Algebraic Proofs

Objective: Solve linear equations using justified steps.

An algebraic proof is a sequence of statements and reasons. Inverse operations preserve equality when applied equally to both sides; simplify expressions before or after a valid operation.

Objective: Justify expanding and simplifying expressions.

The distributive property gives a(b+c)=ab+ac. Combining like terms follows algebraic equivalence; transformation of an equation requires valid operations on both sides.

Objective: Match a proof step with its valid justification.

Each proof statement must follow from prior statements, givens, definitions, or established properties. A proof cannot assume the conclusion or divide by an expression not known to be nonzero.