Linear Inequalities Chapter 5 Class 11 Maths Online Practice Worksheet

Linear Inequalities Class 11 Mathematics — Complete Worksheet Practice Guide

This DigiSadhan online practice worksheet is designed for Class 11 Mathematics Chapter 5, Linear Inequalities. The requested NCERT URL is the official NCERT textbook-access interface; it identifies the textbook PDF area but does not expose the chapter's parsed lesson text in the web page itself. citeturn0view0 This tool therefore provides original practice material around the standard chapter skills rather than copying textbook wording.

1. What Is a Linear Inequality?

A linear inequality compares two linear expressions using symbols such as >, <, ≥ and ≤. Unlike an equation, an inequality usually represents a set of values rather than one single value. The solution set contains every value of the variable that makes the statement true.

Examples: 2x+3>7, 5x−1≤14, and −3x+4≥10.

2. Solving by Transposition

The first step is usually to simplify both sides and collect variable terms on one side. Constants can be moved to the other side using the same addition or subtraction principle used with equations. The key difference appears when multiplying or dividing by a negative number.

If a>b, then a+c>b+c. If a>b and c>0, then ac>bc; if c<0, then ac<bc.

3. The Sign-Reversal Rule

When an inequality is multiplied or divided by a negative number, the inequality symbol must reverse. This is one of the most important rules in the chapter and a frequent source of mistakes.

−2x > 6 ⇒ x < −3.

4. Solution Set

The solution set is the collection of all values satisfying the inequality. For x>3, every real number greater than 3 is a solution. The endpoint 3 is not included. For x≥3, 3 is included as well.

5. Number-Line Representation

Number lines provide a visual way to represent inequalities. An open circle is normally used for a strict inequality such as x>a or x<a. A closed circle is used for an inclusive inequality such as x≥a or x≤a. The shaded direction shows the solution region.

x>a → open endpoint, shade right. x<a → open endpoint, shade left. x≥a → closed endpoint, shade right. x≤a → closed endpoint, shade left.

6. Interval Notation

Interval notation provides a compact description of a solution set. Parentheses indicate excluded endpoints and square brackets indicate included endpoints. For example, x>2 is represented by (2,∞), while x≥2 is [2,∞).

7. Compound Inequalities

Compound inequalities combine two conditions. A statement such as a<x≤b means x is greater than a and less than or equal to b. Its interval notation is (a,b]. Students should carefully check which endpoints are included.

a<x≤b ↔ x∈(a,b].

8. Linear Inequalities with Fractions

Fractions can be removed by multiplying through by a common positive denominator. If the multiplier is negative, the inequality direction must reverse. Keeping track of the sign of every multiplier is essential.

9. Inequalities with Variables on Both Sides

When the variable appears on both sides, bring the variable terms together and constants together. If the resulting coefficient is positive, division preserves the inequality direction; if negative, reverse it. If the variable cancels completely, compare the remaining constants to determine whether every real number or no real number satisfies the statement.

10. Graphical Thinking

Even when a problem is solved algebraically, a quick number-line sketch can verify whether the direction and endpoint are correct. This is particularly helpful after multiplying or dividing by a negative number.

11. Ten-plus Question Types and Sub-parts

1 Basic Inequalities2 Greater Than3 Less Than4 ≥ / ≤5 Brackets6 Variables Both Sides7 Fractional Coefficients8 Interval Notation9 Number-Line Interpretation10 Compound Inequalities11 Positive Variables

Sub-parts: solve one-step inequalities; solve two-step inequalities; collect like terms; transpose constants; handle negative coefficients; solve inequalities with brackets; work with fractional coefficients; identify solution intervals; interpret endpoint inclusion; recognise solution direction; and translate between inequality and interval notation.

12. Difficulty Levels

Easy questions practise direct one- and two-step inequalities, symbols and interval recognition. Medium questions include variables on both sides, brackets and combined steps. Hard questions include fractions, sign changes and multi-step reasoning.

13. Randomized Practice

The tool supports up to 2,000 questions in one worksheet. New tests and Shuffle Whole Worksheet rearrange questions. MCQ choices are also independently randomized, so the correct answer is not permanently placed in Option A.

14. Answer Checking

Students must attempt an answer before seeing the solution. Check Answer provides immediate feedback. Correct answers become green and trigger a celebration animation and sound. Incorrect answers become red and trigger a different animation and sound. Show Answer remains hidden until checking.

15. Timer, Progress and Score

Select no timer or a 5, 10, 15 or 30-minute session. The progress bar shows how many questions have been checked, while the score counts correct responses. Completion displays the final score and percentage.

16. PDF and Print

Save as PDF is a separate download action from Print. The PDF contains the current generated questions and answer spaces. Print uses the browser print facility and is kept separate by design.

17. Mobile-Friendly Student Experience

The layout is mobile-first, with responsive controls, touch-friendly buttons and single-column MCQ choices on small screens. Animated inequality symbols create a friendly visual environment for students without distracting from the mathematics.

18. Smart Revision Method

First master the sign-reversal rule. Then practise one-step and two-step inequalities. Move to variables on both sides and bracketed expressions. Finally revise compound inequalities and interval notation. After every mistake, write the sign rule that should have been used and attempt another shuffled worksheet.

Looking for a free Linear Inequalities Class 11 online practice worksheet? DigiSadhan Chapter 5 Maths worksheet helps students master solution sets, inequality symbols, number-line representation, interval notation, transposition, negative-number sign changes, compound inequalities and multi-step problems. Practise up to 2,000 randomized questions with difficulty levels, MCQ and short-answer modes, instant green/red feedback, progress tracking, timer, sound effects, animations, PDF download and print support—perfect for Class 11 Maths revision on mobile, tablet and desktop.