Inequalities On The Real Number Line
Overview
An equation pins a value down exactly; an inequality describes a whole range of allowed values instead. From speed limits to budgets, much of the real world is governed by 'at least' and 'no more than' rather than exact equality, and inequalities are the mathematics of those limits.
In this lesson you will represent and interpret inequalities on the real number line, and solve linear inequalities. You will see that solving an inequality is almost the same as solving an equation, with one crucial twist when you multiply or divide by a negative number.
Objectives
- Represent and interpret inequalities on the real number line, and (Extended) solve linear inequalities.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Inequalities On The Real Number Line. 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 < 19. A. x < 5 B. x > 5 C. x < 7 D. x > 7 Answer: A
- Solve -2x >= 8. A. x >= -4 B. x <= -4 C. x >= 4 D. x <= 4 Answer: B
- On a number line, x > 3 is shown with: A. A filled circle at 3, arrow left B. An open circle at 3, arrow right C. A filled circle at 3, arrow right D. An open circle at 3, arrow left Answer: B
- When do you reverse the inequality sign? A. When adding a negative B. When dividing by a positive C. When multiplying or dividing by a negative D. Never Answer: C
- Solve 2x - 1 <= 5. A. x <= 2 B. x <= 3 C. x >= 3 D. x < 3 Answer: B
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