Solving Systems of Linear Inequalities

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One thing that puzzles a lot of young algebrists is the factors in a word problem that are taken as "understood". This presentation on solving systems of linear inequalities does a great job walking the learner through how to tease those background constraints out of an inequality word problem. By giving a concrete set of attack strategies and then modeling the strategies in problems, this lesson makes a great add-on to your algebra curriculum.

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CCSS: Adaptable
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Instructional Ideas
  • Link on the class website for an effective before-class presentation in a flipped classroom model or for on-demand homework help in a traditional setting
  • Poll local painting or other hourly service providers in the community to create and solve problems modeled on example 4
  • Divide the class into small groups, and have each group come up with a word problem that would result in the system of inequalities in example 1
  • Brainstorm as a class different situations that would result in a system of inequalities with understood constraints, such as x or y greater than 0
Classroom Considerations
  • Viewing the presentation PowerPoint file requires the ability to open a *.pptx file
  • Internet access and updated Java player needed to use the interactive graphing applet linked in the presentation
  • Working these problems will reveal weaknesses in graphing linear equations and testing points, so consider having remediation handy
  • Detailed description of problem-solving strategies
  • Examples solved step-by-step
  • Common misconceptions and mistakes discussed
  • Both examples contain links to an interactive applet pre-loaded with problem information
  • Two different types of examples demonstrate application of attack methods in a variety of problems
  • Blue and gray opaque shading in the examples makes the overlap set hard to identify, especially since equations aren't graphed in each step
  • The second example is numbered 4 instead of 2
  • No independent practice or homework problems provided