Lesson objective: Students fluently understand that equations can be solved in a variety of ways using operations performed in a different order.

This lesson helps to build fluency with solving linear equations in one variable with one, no, or infinitely many solutions. Equations are used here because they support the problem-solving procedure. This work develops students' understanding that linear equations in one variable may be solved in different orders using the same operations.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they examine equations and their solutions. Students also engage in Mathematical Practice 6 (Attend to precision) as they solve their equations.

**Key vocabulary:**

- infinitely many solutions
- one solution
- no solution
- identical