# Inequalities

## Overview

When delving into the realm of Inequalities in General Mathematics, we are faced with a concept that plays a crucial role in determining the relationship between expressions that are not equal. The objectives of this topic revolve around solving problems related to linear and quadratic inequalities along with interpreting the graphical representation of these inequalities.

Linear inequalities involve expressions that are connected by inequality symbols, typically < (less than), > (greater than), (less than or equal to), or (greater than or equal to). Quadratic inequalities, on the other hand, introduce squared terms, leading to more complex relationships between the variables involved.

One fundamental aspect of inequalities is the ability to represent solutions on a number line. By graphing the solutions to an inequality, students can visually interpret the range of values that satisfy the given conditions. This graphical representation enhances the understanding of the relationship between different expressions and aids in identifying the feasible solutions.

Moreover, the concept of percentage increase and decrease often intertwines with inequalities, as it involves comparing the relative change in values. Understanding how to apply percentage increase and decrease in the context of solving inequalities provides a practical approach to real-life scenarios where such comparisons are essential.

Furthermore, the analytical and graphical solutions of linear inequalities provide students with a comprehensive toolkit to tackle a wide range of mathematical problems. By merging algebraic manipulation with graphical analysis, individuals can effectively determine the solutions to various inequalities, thereby honing their problem-solving skills.

Overall, by mastering the intricacies of inequalities, students develop critical thinking abilities, logical reasoning skills, and a deeper understanding of mathematical relationships. The journey through this topic equips learners with the tools necessary to navigate through complex mathematical landscapes and apply their knowledge to both theoretical and practical scenarios.

## Objectives

1. Interpret Graphs of Inequalities
2. Solve Problems on Linear and Quadratic Inequalities

## Lesson Note

For example, x < 3 is represented by a hollow circle at 3 with a line extending to the left.

## 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.

1. Solve the following inequality: 2x + 3 < 7 A. x < 2 B. x > 2 C. x < 1 D. x > 1 Answer: A. x < 2
2. Solve the inequality: 4 – 2x ≥ 8 A. x ≤ -2 B. x ≥ -2 C. x ≤ 3 D. x ≥ 3 Answer: A. x ≤ -2
3. Which of the following represents the solution set of the inequality -3x + 5 < 8? A. x > -1 B. x < -1 C. x > 1 D. x < 1 Answer: A. x < -1
4. If 3x - 2 > 10, then x is A. x > 4 B. x < 4 C. x > 6 D. x < 6 Answer: C. x > 6
5. Solve the inequality: 2(x + 5) ≤ 12 A. x ≥ -4 B. x ≤ -4 C. x ≥ 1 D. x ≤ 1 Answer: A. x ≥ -4
6. Which of the following is the solution to the inequality 2x + 4 > 10? A. x > 3 B. x < 3 C. x > 1 D. x < 1 Answer: A. x > 3
7. Determine the solution for the inequality: 3(x - 2) ≤ 9 A. x ≤ 5 B. x ≥ 5 C. x ≥ 3 D. x ≤ 3 Answer: B. x ≥ 5
8. If 2x + 3 > 7, then x is: A. x > 2 B. x < 2 C. x > 3 D. x < 3 Answer: B. x < 2
9. Find the solution set for the inequality: 5x - 3 > 12 A. x > 3 B. x < 3 C. x > 3 D. x < 3 Answer: D. x < 3
10. Solve the inequality: 2(x - 4) ≤ 3x + 1 A. x ≥ -3 B. x ≤ -3 C. x ≥ 3 D. x ≤ 3 Answer: C. x ≥ 3

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Inequalities from previous years

Question 1

If x varies over the set of real numbers, which of the following is illustrated in the diagram above?

Question 1

Determine the area of the region bounded by:

Question 1

Twice a number, x, is added to 5, the result is at least 11. What is the range of values of x?

Practice a number of Inequalities past questions