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.
Lesson overview
 20.1 Warmup: Dinner for Drama Club (5 minutes)
 20.2 Activity: Gasoline in the Tank (10 minutes)

20.3 Activity: Different Ways of Solving (20 minutes)
 Includes "Are you Ready for More?" extension problem
 20.4 Optional Activity: Matching Inequalities and Solutions (15 minutes)
 Lesson Synthesis
 20.5 Cooldown: How Many Hours of Work? (5 minutes)
Learning goals:
 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.
Learning goals (student facing):
 Let’s solve problems by writing and solving inequalities in one variable.
Learning targets (student facing):
 Let’s solve problems by writing and solving inequalities in one variable.
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