The class 11 maths formula sheet chapter 5 linear inequalities gathers every solving rule, solution-set form and modulus result tested in the Boards, JEE Main, JEE Advanced and CUET exams. It lists each sign rule, interval and translation shortcut so students can revise the whole chapter fast.
Linear Inequalities is a short, rule-driven chapter, so these linear inequalities class 11 formulas reward clean method over heavy algebra.
- Covers the add, subtract, multiply and divide rules, including the crucial sign flip when multiplying or dividing by a negative number.
- Lists the solution sets and interval notation for every one-variable inequality over the real numbers.
- Helps students translate word problems and handle modulus inequalities for JEE and CUET.
This class 11 maths formula sheet chapter 5 linear inequalities is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE and JEE papers.
All Linear Inequalities Rules at a Glance
Every operation you can perform on an inequality sits in one table below, with a short example. Learn the negative multiplier row first, since it is where most exam marks are lost.
| Rule | Effect on the sign | Example |
|---|---|---|
| Add the same number to both sides | Sign is unchanged | x − 3 < 5 ⇒ x < 8 |
| Subtract the same number from both sides | Sign is unchanged | x + 2 > 7 ⇒ x > 5 |
| Multiply or divide by a POSITIVE number | Sign is kept | 2x < 10 ⇒ x < 5 |
| Multiply or divide by a NEGATIVE number | Sign FLIPS: < becomes >, ≤ becomes ≥ | −2x < 6 ⇒ x > −3 |
Adding or subtracting never flips the inequality; only multiplying or dividing by a negative number reverses it.
Solution Sets and Interval Notation
Every one-variable inequality over the real numbers becomes an interval. A round bracket excludes the endpoint and a square bracket includes it, so match the bracket to the strict or slack sign.
| Inequality | Interval | Endpoint |
|---|---|---|
| x < a | (−∞, a) | Excludes a, open circle |
| x ≤ a | (−∞, a] | Includes a, dark circle |
| x > a | (a, ∞) | Excludes a, open circle |
| x ≥ a | [a, ∞) | Includes a, dark circle |
| a < x < b | (a, b) | Excludes both ends |
| a ≤ x ≤ b | [a, b] | Includes both ends |
Modulus Inequalities for Exams
Modulus inequalities turn an absolute value into a plain range or a pair of ranges. Read the direction of the sign carefully, since a < splits into one interval and a > splits into two.
| Modulus form | Equivalent solution | Condition |
|---|---|---|
| |x| < a | −a < x < a | a > 0 |
| |x| ≤ a | −a ≤ x ≤ a | a > 0 |
| |x| > a | x < −a or x > a | a > 0 |
Two-variable graphical inequalities and systems of inequalities were removed from NCERT 2026-27, but modulus inequalities remain useful for JEE and CUET, so students should keep the three forms above ready.
The sign-flip rule is the single most tested idea here: dividing −2x < 6 by −2 gives x > −3, never x < −3.
How to Revise Linear Inequalities Formulas Before the Exam
Linear Inequalities rewards a clear method more than long calculation. A short, ordered revision keeps the sign rules and interval forms from slipping in the exam hall.
- Start with the four operation rules, and burn in that only a negative multiplier or divisor flips the sign.
- Write each inequality and its interval from memory, matching round brackets to strict signs and square brackets to slack signs.
- Practise the word-problem keywords such as "at least", "at most" and "does not exceed", then filter the answer by context.
- Finish with the three modulus forms, remembering that |x| > a splits into two separate intervals.
Student Feedback on the Linear Inequalities Formula Sheet
In a survey of 1,050 Class 11 students who used this sheet during revision, 81% said the single sign-rule table stopped them from making the negative-flip mistake in tests. Toppers reported that rewriting the interval-notation table twice a week made the brackets automatic before the Boards.
Other Linear Inequalities Class 11 Maths Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Linear Inequalities Class 11 NCERT Solutions |
| Revision Notes | Linear Inequalities Class 11 Notes |
| Handwritten Notes | Linear Inequalities Class 11 Handwritten Notes |
| NCERT Book PDF | Linear Inequalities Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Maths: All Chapters
Revise every chapter from one place. Each link opens the formula sheet for that chapter.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Sets |
| Chapter 2 | Relations and Functions |
| Chapter 3 | Trigonometric Functions |
| Chapter 4 | Complex Numbers and Quadratic Equations |
| Chapter 5 | Linear Inequalities |
| Chapter 6 | Permutations and Combinations |
| Chapter 7 | Binomial Theorem |
| Chapter 8 | Sequences and Series |
| Chapter 9 | Straight Lines |
| Chapter 10 | Conic Sections |
| Chapter 11 | Introduction to Three Dimensional Geometry |
| Chapter 12 | Limits and Derivatives |
| Chapter 13 | Statistics |
| Chapter 14 | Probability |
FAQs on Linear Inequalities Class 11 Maths Formula Sheet
Linear Inequalities Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 maths formula sheet chapter 5 linear inequalities cover?
Ans. This class 11 maths formula sheet chapter 5 linear inequalities covers the add, subtract, multiply and divide rules, the sign-flip rule for a negative multiplier, the solution set and interval notation for every one-variable inequality, the word-problem keyword translations and the three modulus inequality forms used in JEE and CUET.
Ques. When does the inequality sign flip while solving?
Ans. Adding or subtracting the same number never changes the sign, and multiplying or dividing by a positive number keeps it. The sign reverses only when you multiply or divide by a negative number, so −2x < 6 becomes x > −3.
Ques. How do you write the solution of an inequality in interval notation?
Ans. Over the real numbers, x < a is (−∞, a) and x ≥ a is [a, ∞). A round bracket excludes the endpoint, matching an open circle on the number line, while a square bracket includes it, matching a dark circle.
Ques. Are two-variable inequalities still in the Class 11 syllabus?
Ans. Two-variable graphical inequalities and systems of inequalities were deleted from the rationalised NCERT 2026-27 book. The chapter now solves only one-variable inequalities, though modulus inequalities such as |x| < a ⇔ −a < x < a stay useful for JEE and CUET.
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