Lesson objective: Students fluently understand that not every equation has a solution; some have no solution, some have one solution, and some have infinitely many solutions.

This lesson helps to build fluency with solving linear equations in one variable with no solution, one solution, 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 have no solution, one solution, or infinitely many solutions.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they examine equations and their solutions.

**Key vocabulary:**

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