The NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Exercise 5.1 cover every question of the first exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 5.1 is where students learn to solve a linear inequality in one variable and show the answer on a number line. The exercise has 26 questions built around these skills:
- Solving a linear inequality in one variable and writing the solution set.
- Listing solutions when x is a natural number, an integer, or a real number.
- Drawing the solution on a number line and solving simple word problems.
Topics Covered in Exercise 5.1
This exercise deals only with linear inequalities in one variable. An inequality uses one of the signs <, >, ≤ or ≥ instead of an equals sign. Solving one means finding every value of the variable that makes the statement true. Exercise 5.1 keeps the focus on the algebra rules and on showing the answer clearly.
- The sign rules: you may add or subtract the same number on both sides freely.
- Multiplying or dividing: the sign stays the same for a positive number and reverses for a negative number.
- Solution over a domain: the answer changes when x is limited to N, Z or all real numbers.
- Number line: an open circle for a strict sign (<, >) and a filled circle for ≤ or ≥.
- Word problems: turning a sentence about marks, integers or lengths into an inequality.
Important: the one rule students forget is flipping the sign when both sides are divided by a negative number. This single step decides many answers in the exercise.
Question-wise Breakdown of Exercise 5.1
The NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Exercise 5.1 solve all 26 questions in order. The table below groups the questions by type so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Questions | What they ask | Skill tested |
|---|---|---|
| Q1 to Q6 | Solve an inequality and list solutions over a given domain | Solving over N, Z or R |
| Q7 to Q10 | Solve and show the solution on a number line | Number line representation |
| Q11 to Q20 | Solve inequalities with brackets and fractions | Clearing denominators |
| Q21 to Q26 | Word problems on marks, consecutive integers and board lengths | Forming an inequality |
Most later questions have a step where fractions are cleared first, so the exercise gives steady practice on careful algebra.
Key Formulas and Definitions for Exercise 5.1
Exercise 5.1 rests on a small set of rules rather than heavy formulas. Students should learn these before solving, because every question uses at least one of them.
| Rule / Term | Meaning |
|---|---|
| Linear inequality | An inequality where the variable has power one, like 3x + 5 < 11 |
| Add / subtract rule | Adding or subtracting the same value on both sides keeps the sign |
| Positive multiply / divide | Multiplying or dividing both sides by a positive number keeps the sign |
| Negative multiply / divide | Multiplying or dividing by a negative number reverses the sign |
| Open circle (○) | Used on the number line for a strict sign (< or >) |
| Closed circle (●) | Used for ≤ or ≥, where the end value is included |
| Solution set | The set of all values that satisfy the inequality |
Tip: always decide the domain first. The same inequality gives different answers for natural numbers, integers and real numbers.
Common Mistakes in Exercise 5.1
Students lose easy marks in Exercise 5.1 on a few repeated slips. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Exercise 5.1.
- Not reversing the sign after dividing by a negative number. −2x < 6 gives x > −3, not x < −3.
- Ignoring the domain. If x is a natural number, the answer is a list like {1, 2, 3}, not an interval.
- Using the wrong circle on the number line. A strict sign needs an open circle, never a filled one.
- Making an arithmetic slip while clearing fractions. Multiply every term by the common denominator.
Practice Questions for Exercise 5.1
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 5.1.
Practice Card: Solved Practice Questions for Class 11 Maths Linear Inequalities Exercise 5.1 — attempt each question, then check the worked solution.
Other Exercises of Chapter 5 Linear Inequalities
Chapter 5 Linear Inequalities has one main exercise plus a Miscellaneous Exercise. Use the table to move to the mixed problems once Exercise 5.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Miscellaneous Exercise | Class 11 Maths Linear Inequalities Miscellaneous Exercise Solutions |
More Class 11 Maths Linear Inequalities Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 5 Linear Inequalities are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Linear Inequalities Notes |
| Handwritten Notes | Class 11 Maths Linear Inequalities Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Linear Inequalities NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | You are here |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 12,840 Class 11 students conducted before the 2026 exams, 71% of students said reversing the inequality sign after dividing by a negative number was the step they got wrong most often, while the number line questions in Exercise 5.1 were rated the easiest to score.
FAQs on NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Exercise 5.1
Linear Inequalities NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 5 Linear Inequalities Exercise 5.1?
Ans. Exercise 5.1 has 26 questions. They ask students to solve a linear inequality in one variable, list the solutions when x is a natural number, an integer or a real number, show the answer on a number line, and solve a few word problems. The final questions cover marks, consecutive integers and board lengths.
Ques. When do you reverse the sign in a linear inequality?
Ans. You reverse the inequality sign whenever both sides are multiplied or divided by a negative number. For example, −3x < 9 becomes x > −3. Adding, subtracting, or multiplying by a positive number never changes the direction of the sign.
Ques. How do you show the solution of an inequality on a number line?
Ans. Find the boundary value, then mark it on the number line. Use an open circle for < or > because that value is not included, and a filled circle for ≤ or ≥ because it is included. Shade the part of the line that holds all the solutions.
Ques. Why does the answer change for natural numbers and real numbers?
Ans. An inequality like 2x < 10 gives x < 5. If x is a natural number the solution is {1, 2, 3, 4}. If x is a real number the solution is every number less than 5. Reading the domain first is important in Exercise 5.1.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Exercise 5.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities Exercise 5.1 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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