# Lesson 16

Interpreting Inequalities

### Lesson Narrative

In this lesson and the next, we move on to applying inequalities to solve problems. The warm-up is a review of the work in the previous lesson about solving inequalities when no context is given. Then students interpret and solve inequalities that represent real-life situations, making sense of quantities and their relationships in the problem (MP2).

### Learning Goals

Teacher Facing

• Critique (orally) a solution method for a problem involving an inequality.
• Identify the inequality that represents a situation, and justify (in writing) the choice.
• Present (orally, in writing, and using other representations) the solution method for a problem involving an inequality, and interpret the solution.

### Student Facing

Let’s write inequalities.

### Student Facing

• I can match an inequality to a situation it represents, solve it, and then explain what the solution means in the situation.
• If I have a situation and an inequality that represents it, I can explain what the parts of the inequality mean in the situation.

Building Towards

### Glossary Entries

• solution to an inequality

A solution to an inequality is a number that can be used in place of the variable to make the inequality true.

For example, 5 is a solution to the inequality $$c<10$$, because it is true that $$5<10$$. Some other solutions to this inequality are 9.9, 0, and -4.