Final answer:
Algebraic properties are used to solve one-variable equations through deductive reasoning, leveraging established properties like the associative and commutative to justify steps solving the equation.
Step-by-step explanation:
Algebraic properties are used to justify a method for solving a one-variable equation primarily based on logical reasoning. This involves the use of deductive thinking, which leverages established algebraic properties such as the associative, commutative, and distributive properties to manipulate equations.
For instance, a step-by-step method for solving a one-variable equation might start with listing what is known and unknown (the givens and the variables), then finding an appropriate equation or set of equations containing only one unknown, and substituting known values to solve for the unknown. Checking if the answer is reasonable is an essential final step in the process.