# Lesson 23

Solving Problems with Inequalities in Two Variables

### Lesson Narrative

By now students recognize that solutions to linear inequalities can be found by graphing, and that this can be done by first graphing a related equation and deciding on the solution region. In this lesson, they learn to use graphing technology to find the solution set of a linear inequality in two variables.

Students then use this skill to solve problems that involve inequalities. They write linear inequalities to represent the constraints in situations and then use the representations (including the graphs of the solutions) to answer questions about the situations. As they write inequalities from descriptions, decide on the solution sets, and interpret points in a solution region, students engage in quantitative and abstract reasoning (MP2).

### Learning Goals

Teacher Facing

• Identify an inequality, a graph, an ordered pair, and a description that represent the constraints and possible solutions in a situation.
• Understand that a constraint on two variables can be represented by an inequality, a graph (a half-plane), and a verbal description.
• Write inequalities in two variables to represent the constraints in a situation and use technology to graph the solution set to answer questions about the situation.

### Student Facing

• Let’s practice writing, interpreting, and graphing solutions to inequalities in two variables.

### Required Preparation

Print and cut up slips from the blackline master. Prepare 1 copy for every 2 students.

Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (If students typically access the digital version of the materials, Desmos is always available under Math Tools.)

### Student Facing

• I can use graphing technology to find the solution to a two-variable inequality.
• When given inequalities, graphs, and descriptions that represent the constraints in a situation, I can connect the different representations and interpret them in terms of the situation.