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Unit 2 — Inequalities

Unit 2 · Inequalities

Inequalities

Write, solve, and graph one-step, two-step, and compound inequalities. Apply inequality reasoning to real-world problems.

Estimated Time

25–35 minutes

Difficulty

Easy

8 Lessons
6 Learning Goals
10 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 2 — Inequalities extends your equation-solving skills into the world of inequalities. You will write, solve, and graph one-step, two-step, and compound inequalities, work with integers, fractions, and decimals, and apply inequality reasoning to real-world problems.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Understand inequality symbols and graph solution sets on a number line.
Goal 2Solve one-step and two-step inequalities using inverse operations, flipping the symbol when multiplying or dividing by a negative.
Goal 3Solve and graph compound inequalities joined by AND (intersection) or OR (union).
Goal 4Solve absolute value equations using the Two-Case Method and absolute value inequalities using the Less-Than and Greater-Than rules.
Goal 5Graph linear inequalities in two variables by shading the correct half-plane on the coordinate plane.
Goal 6Write solutions in interval notation and apply inequality reasoning to real-world problems.

Skills You Will Master

Solving inequalities with inverse operations
Compound inequalities (AND / OR)
Absolute value equations and inequalities
Graphing on number lines and coordinate planes
Interval notation and real-world applications

Real-World Connection

Inequalities are everywhere in daily life. Speed limits, budget constraints, safety thresholds, and quality-control tolerances are all modeled by inequalities. When an engineer specifies that a bolt must be within 0.02 mm of a target length, they are writing an absolute value inequality. When a business sets a minimum order quantity, that is a one-step inequality. Mastering inequalities gives you the tools to describe, analyze, and solve any situation where a range of values — not just a single answer — is the goal.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter
Unit 2Unit Overview2.1 · Introduction to Inequalities