Variables on Both Sides

Objective: Explain and use collecting variable terms in an Algebra 1 problem.

Subtracting the same variable term from both sides moves all variable terms to one side without changing the solution set. Unequal operations change the equation.

Objective: Explain and use one solution in an Algebra 1 problem.

A linear equation that reduces to a nonzero multiple of x equal to a constant has one solution over the real numbers. Substitute it into both original sides.

Objective: Explain and use identity and contradiction in an Algebra 1 problem.

A true statement such as 0=0 after simplification signals infinitely many solutions in the domain; a false one such as 0=5 signals no solution. There is no solution if the transformations were equivalent.