# Lesson 20

Writing and Solving Inequalities in One Variable

### Lesson Narrative

This lesson serves two main goals. The first is to prompt students to write and solve inequalities to answer questions about a situation. They consider not only whether the inequalities appropriately model the situations, but also whether there are assumptions that need to be stated and whether the solution sets make sense in context. Along the way, they practice reasoning quantitatively and abstractly (MP2) and engage in aspects of mathematical modeling (MP4).

The second goal is to practice finding the solution set to an inequality by reasoning about its composition and parts. Take $$0.5x > 10x$$ for example. We can reason that for 0.5 times a number to be greater than 10 times the same number, the number must be negative, so the solution is $$x<0$$. Likewise, we can see that all values of $$x$$ are solutions to $$x < x + 5$$ because 5 more than a number will always be greater than that number. Students practice looking for and making use of structure (MP7) as they reason about solutions this way.

The lesson includes an optional activity for practice solving inequalities without a context.

### Learning Goals

Teacher Facing

• Analyze and use the structure in inequalities to determine whether the solution is greater or less than the solution to a related equation.
• Write and solve inequalities in one variable to represent the constraints in situations and to solve problems.

### Student Facing

• Let’s solve problems by writing and solving inequalities in one variable.

### Student Facing

• I can analyze the structure of an inequality in one variable to help determine if the solution is greater or less than the solution to the related equation.
• I can write and solve inequalities to answer questions about a situation.