Lesson objective: Students understand that equations can be solved by writing a succession of equivalent equations.

Students bring prior knowledge of solving equations from 7.EE.A.1 and 7.EE.A.2. This prior knowledge is extended to solving linear equations in one variable as students explore linear equations in one variable with no solution, one solution, and infinitely many solutions. A conceptual challenge students may encounter is understanding the difference between what the solutions to equations with no solution and those with infinitely many solutions look like.

The concept is developed through examination of equations in varying states of solving, which illustrates the difference between equations with one, none and infinitely many solutions.

This work helps students deepen their understanding of operations because they will apply properties of operations to a variety of equations.

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