Lesson objective: Understand that inequalities can be solved using inverse operations to write equivalent inequalities leading to a solution.

Students bring prior knowledge of solving equations from 7.EE.B.4.a. This prior knowledge is extended to inequalities as students learn how to solve inequalities. A conceptual challenge students may encounter is that although the process is primarily the same, the solution is different than that of an equation.

The concept is developed through work with number lines, which helps to support the understanding of the difference between the solution to an equation and the solution to an inequality.

This work helps students deepen their understanding of equivalence because each inequality must be equivalent to the one that came before it.

Students engage in Mathematical Practice 1 and 4 (Make sense of problems and perservere in solving them and Model with mathematics) as they struggle to develop an algebraic model to represent a complex situation and to find a solution that fits both the model and the context of the situation.

**Key vocabulary:**

- equation
- inverse
- isolate
- operations
- solution