Inequalities
Overview
An inequality says that one quantity is less than, or greater than, another, rather than exactly equal. Speed limits, minimum ages, budget ceilings and safe ranges are all inequalities, and they describe the world far more often than tidy equalities do.
In this lesson you will represent inequalities on a number line, then at Extended level construct and solve linear inequalities, solve them with a graphic display calculator, and picture linear inequalities in two variables as regions on a graph. You will also learn to read off the inequalities that define a shaded region.
Objectives
- Represent and interpret inequalities, including on a number line.
- Construct, solve and interpret linear inequalities. (Extended only)
- Solve inequalities using a graphic display calculator. (Extended only)
- Represent and interpret linear inequalities in two variables graphically. (Extended only)
- List inequalities that define a given region. (Extended only)
Audio Lesson
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Mind map
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Flashcards
Quick recall practice on the facts this topic is tested on.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Inequalities. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Solve 3x - 4 < 11. A. x < 5 B. x > 5 C. x < 7 D. x > 7 Answer: A
- Solve -2x >= 6. A. x >= 3 B. x <= 3 C. x >= -3 D. x <= -3 Answer: D
- On a number line, which circle marks a value that is included, as in x >= 2? A. an open circle B. a filled circle C. an arrow only D. a dashed circle Answer: B
- When drawing the region for y < 2x + 1, the boundary line should be: A. solid B. dashed C. dotted and shaded D. omitted Answer: B
- Is the origin (0, 0) in the region y < 2x + 1? A. Yes B. No C. Only on the line D. Cannot tell Answer: A
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Recommended Books
Practice Mock Questions
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