Inequalities in Maths (original) (raw)
Inequalities are mathematical expressions that show the relationship between two values when they are not equal, i.e., one side can be greater or smaller than the other. We use inequalities in our daily lives in many places, such as:
- You must be at least 18 years old to vote, i.e., age ≥ 18 for voting.
- The speed limit on the highway is 65 mph. This means you must drive at or below 65 mph: Speed ≤ 65
- You must be at least 48 inches tall to ride this rollercoaster.
- To qualify for a loan, your income must be higher than $40,000 per year.
Mathematical expressions in which the LHS and RHS are unequal i.e., one is greater than the other or one is smaller than the other, are called inequalities.
Foundations
Learn the core concepts and notation to build a strong base.
- Introduction to Inequalities
- Linear Inequalities
- Interval Notation
- Inequality in Reasoning
- Representation of Inequalities on Number Line
**Linear Inequalities in One Variable
Understand and solve inequalities involving a single variable.
- Linear Inequalities
- Solving Inequalities
- Solve Inequalities with Addition and Subtraction
- Solve Linear Inequalities
- Compound Inequalities
- Absolute Value Inequalities
- Algebraic Solutions of Linear Inequalities in One Variable
Inequalities in Two Variables
Extend inequality concepts to two-variable expressions and graphs.
Systems of Inequalities
Work with multiple inequalities together and find common solution regions.
- System of Inequalities
- Graphical Solution of System of Linear Inequalities
- Quadratic Inequalities
- How to Solve Quadratic Inequalities
Important Theorems
Explore key theorems and classical results built on inequalities.
Practice
Test your understanding with word problems and practice questions.