Linear Equations, Inequalities and Systems

Lesson 8


Write linear inequalities from contextual situations.

Common Core Standards

Core Standards


  • A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Foundational Standards


  • 8.F.B.4

  • 8.F.B.5

Criteria for Success


  1. Identify features of linear inequalities from word problems and represent them algebraically. 
  2. Describe linear inequalities as “constraints” in the problem. Describe how these inequalities restrict the possible solutions to the problem.
  3. Graph linear inequalities from contextual situations and describe solutions in the context of the problem. 

Anchor Problems


Ms. Larkin is organizing an optional field trip for eighth graders and staff to see a play at the Wang Center. She is able to get a discounted price on the tickets: student tickets are $6 each, and adult tickets are $8 each. If Ms. Larkin has a budget of $240, then what different combinations of students and adults can go on the trip?

Guiding Questions

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Problem Set


The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include problems where the inequality is presented verbally (e.g., a number times 3 is less than another number) and students are required to graph and identify solutions. 

Target Task


Beverly is serving hamburgers and hot dogs at her cookout. Hamburger meat costs $3 per pound, and hot dogs cost $2 per pound. She wants to spend no more than $30.

  1. Write an inequality to describe the situation.
  2. Graph the solutions on a coordinate plane. 

  1. Give two combinations of pounds of hamburger and hot dogs that Beverly can buy.