# Linear Inequalities Assignments/DPPs

Linear inequalities , a cornerstone of mathematical modeling, form a vital chapter in Class 11 and a crucial foundation for the Joint Entrance Examination (JEE). Understanding how to represent and solve inequalities empowers you to analyze and interpret real-world scenarios involving relationships between variables.

## Overview of Linear Inequalities

#### Understanding Linear Inequalities:

• Definition: An inequality is a mathematical statement expressing that two expressions are not equal. When these expressions involve linear functions, they are termed linear inequalities.
• Representation: Linear inequalities are represented using symbols like `<` (less than), `>` (greater than), `≤` (less than or equal to), and `≥` (greater than or equal to).
• Form: They are generally expressed in the form `ax + b < (≤, >, ≥) c`, where a, b, and c are real numbers, and a ≠ 0.

#### Key Formulas and Properties:

• Adding/subtracting constants: Add or subtract the same constant to both sides without affecting the inequality.
• Multiplying/dividing by a positive constant: Multiply or divide both sides by the same positive constant, keeping the inequality sign the same.
• Multiplying/dividing by a negative constant: Multiply or divide both sides by the same negative constant, and reverse the inequality sign.

#### Solving Linear Inequalities:

1. Isolate the variable: Use algebraic operations to bring the variable to one side of the inequality.
2. Consider the sign of the coefficient: Depending on the coefficient and the applied operation, the inequality sign might need to be reversed.
3. Express the solution in interval notation: Represent the set of all possible solutions as an interval on the number line.

#### Question Types in the JEE:

The JEE tests your understanding of linear inequalities through diverse question types, including:

• Solving single variable inequalities: Finding the range of values for a variable that satisfies the given inequality.
• Solving systems of inequalities: Finding solutions that satisfy multiple inequalities simultaneously.
• Word problems: Applying linear inequalities to model and solve real-world scenarios involving quantities, rates, and other relationships.

## DPPs for Linear Inequalities

Mastering Linear Inequalities with PRERNA EDUCATION:

• Targeted assignments: Strengthen your grasp of key concepts by practicing diverse problems from the targeted assignments offered by PRERNA EDUCATION.
• Daily Practice Problems (DPPs): Hone your problem-solving skills and build speed by tackling daily practice problems (DPPs) encompassing various difficulty levels and solution techniques.
• Expert guidance: Don’t hesitate to seek clarification from teachers or utilize online resources provided by PRERNA EDUCATION for additional insights and explanations.
• Visualize the solution: Utilize number lines to represent inequalities graphically, helping you visualize the solution set and verify your answers.

Embrace the Challenge:

Linear inequalities might seem straightforward at first, but mastering them requires dedicated practice and a clear understanding of the underlying concepts. By leveraging the resources offered by PRERNA EDUCATION, consistently practicing with diverse problems, and seeking help when needed, you can conquer this chapter and excel in Class 11 and your JEE preparation. Remember, a positive learning approach, active engagement, and a willingness to learn are key to achieving success.

 Reach Us 011 – 41659551 | 9312712114  CENTERS H-81, South Extension Part 1, New Delhi – 110049 179, 2nd Floor, opposite Select Citywalk Mall, Khirki Village, Saket, New Delhi – 110017 Phone: 011-41659551 | 011-41676717 Mobile: +91-9312712114 Email: info@prernaeducation.co.in