# Lesson 17

Modeling with Inequalities

### Lesson Narrative

By now, students have had plenty of experience writing and solving inequalities. This lesson focuses on the modeling process (MP4), in which students start with a question they want to answer and decide on their own how they will represent the situation mathematically.

As students apply inequalities in context, they must think about how to interpret their solutions. For instance, if they find that $$x<7$$, but $$x$$ represents the number of students who can go on a trip, then they should realize that $$x$$ cannot be 3.25, nor can $$x$$ be -2.

### Learning Goals

Teacher Facing

• Critique (orally) the solution to an inequality, including whether fractional or negative values are reasonable.
• Determine what information is needed to solve a problem involving a quantity constrained by a maximum or minimum acceptable value. Ask questions to elicit that information.
• Write and solve an inequality of the form $px+q \gt r$ or $px+q \lt r$ to answer a question about a situation with a constraint.

### Student Facing

Let's look at solutions to inequalities.

### Required Preparation

Print and cut up copies of the blackline master for the Giving Advice activity. You will need one set of cards for every 4 students.

### Student Facing

• I can use what I know about inequalities to solve real-world problems.

### CCSS Standards

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.