Introduction to Inequalities

Introduction to Inequalities

• Inequalities are mathematical statements that compare two expressions using inequality symbols.
• These symbols include "greater than" (>), "less than" (<), "greater than or equal to" (≥), and "less than or equal to" (≤).
• Unlike equations, which state that two expressions are equal, inequalities show that one expression is greater than, less than, or unequal to another.

Types of Inequalities

• Inequalities can involve variables (letters representing unknown values).
• For example, x > 5 means that x is a number greater than 5.
• Inequalities can also involve numbers only, such as 3 < 7.

Solving Inequalities

• The goal in solving an inequality is to isolate the variable to understand the range of values it can take.
• The rules for solving inequalities are similar to those for solving equations.
• However, there's a crucial difference: if you multiply or divide both sides by a negative number, you must flip the inequality sign.

Graphing Inequalities

• Inequalities can be represented on a number line.
• An open circle on the number line indicates a "greater than" or "less than" relationship (not inclusive).
• A closed circle indicates a "greater than or equal to" or "less than or equal to" relationship (inclusive).
• An arrow indicates the direction of the numbers that satisfy the inequality.

Examples of Simple Inequalities

• x + 3 > 7
• 2x ≤ 10
• y - 5 < 2
• y ≥ - 1

Using Inequalities in Real-World Situations

• Inequalities are useful for representing situations involving comparisons.
• For example, "You must be at least 16 years old to drive" can be written as age ≥ 16.
• "The temperature must not exceed 30°C" can be written as temperature ≤ 30°C.

Representing Inequalities on a Number Line

• Representing inequalities on a number line involves using appropriate symbols (open or closed circles) and arrows to indicate the solutions.
• Plotting solutions on the number line demonstrates the range of values that satisfy the inequality.

This quiz covers the basics of inequalities in mathematics, including how to interpret and solve them. Explore types of inequalities, inequality symbols, and the rules for isolating variables. Test your understanding of these fundamental concepts to strengthen your math skills.