Lesson 3: Solving Inequalities-Applications

What are the given information?
what is the word problem asking you?

translate real-world situations into inequalities, solve those inequalities algebraically, and then visually represent the solution set on a graph, often including interpreting the shaded region within the context of the problem

Lesson Description: This lesson focuses on the modeling and solving of contextual problems using linear inequalities. Students will learn to translate specific "threshold" language into the correct inequality symbols. The lesson covers: Translation of limits: Identifying "no more than" (<=), "at least" (>=), "fewer than" (<), and "exceeds" (>).Budgeting and Profit: Setting up inequalities to find the minimum number of units to sell or maximum items to buy within a fixed cost. Average Grade Problems: Calculating the minimum score needed on a final exam to achieve a specific course grade (e.g., "What score do you need to maintain an average of at least 80?").Constraint Analysis: Ensuring the solution makes sense (e.g., you cannot sell a negative number of items).
Purpose: The purpose of this section is to develop decision-making logic. In the real world, problems rarely have a single "equals" answer; they usually involve finding a range of acceptable options. By working through these applications, students learn to use algebra to set boundaries and make informed choices. This is a critical skill for any student heading into business, nursing, or technology fields where "safety margins" and "budget ceilings" are daily realities.
Depth of Knowledge (DOK) Level
DOK Level 2 & 3
Level 2 (Skills and Concepts): Translating real-world phrases into mathematical symbols and solving the resulting inequality using established algebraic steps.
Level 3 (Strategic Thinking/Complex Reasoning): Students must interpret the meaning of the solution set in a physical context. For example, if a solution is x > 4.2 but x represents "number of people," the student must reason that the answer starts at 5. It requires evaluating the "reasonableness" of the interval and justifying why one direction of the inequality was chosen over the other.

classwork and online work

"you try" on page 106 and practice problems