# Linear Inequalities Notes, Class 11 Mathematics | SwaVid Linear Inequalities, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/linear-inequalities Source: https://www.swavid.com/cbse/class-11/maths/chapter/linear-inequalities # Linear Inequalities ## Formulas and definitions ## Key ideas ## Common mistakes ## Quick checks ## Keep going ## Questions parents ask ## Class 11 Mathematics on SwaVid ### Inequalities and notations ### Addition and subtraction rule ### Multiplication and division by positive numbers ### Multiplication and division by negative numbers ### Solution set and interval notation ### Next chapter ### Related chapter ### Related chapter ### Related chapter ### All chapters SwaVid › CBSE › Class 11 › Mathematics › Linear Inequalities Notes written by SwaVid from the NCERT textbook. Class 11 Mathematics, Chapter 5. Key ideas, formulas and common mistakes. CBSE does not print marks for a single chapter. Short answer. This chapter explains algebraic statements that use inequality symbols rather than equality signs to relate real quantities. Students learn how to solve linear inequalities in one variable and represent their solution sets using intervals and number lines. Source: NCERT Mathematics (Reprint 2026-27) , Chapter 5, Linear Inequalities Two real numbers or algebraic expressions related by the symbols , ≤, or ≥ form an inequality. Inequalities involving are strict inequalities, while those involving ≤ or ≥ are slack inequalities. Equal numbers may be added to or subtracted from both sides of an inequality without changing the sign of inequality. This rule mirrors the balance property used for ordinary algebraic equations. Both sides of an inequality can be multiplied or divided by the same positive number without affecting the inequality sign. The direction of the inequality remains completely unchanged. When both sides of an inequality are multiplied or divided by a negative number, the sign of inequality must be reversed. For example, less than becomes greater than. The values of the variable that make an inequality a true statement form its solution set. Solutions over real numbers are written in interval notation, using round brackets for excluded values and square brackets for included values. Try each question first. Then tap it to see the answer. Divide both sides by 30: x -2 (-2, ∞) Multiply all terms by the LCM 6: 2(5 - 2x) ≤ x - 30 Expand brackets: 10 - 4x ≤ x - 30 Subtract x from both sides: 10 - 5x ≤ -30 Subtract 10 from both sides: -5x ≤ -40 Divide both sides by -5 and reverse the inequality sign: x ≥ 8 [8, ∞) Permutations and Combinations . Sets . Relations and Functions . Straight Lines . The 14 chapters of Class 11 Mathematics . The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment. No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed. Permutations and Combinations. SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works. - Ch 5 NCERT book - 80 marks, theory paper - 3 quick checks - Forgetting to reverse the inequality sign when dividing or multiplying by a negative number . Always flip the inequality sign whenever both sides are multiplied or divided by a negative quantity, such as changing -2x -3. - Cross-multiplying expressions with variables whose sign is unknown . Do not multiply across an inequality by a variable expression unless you are sure of its sign. Move terms to one side and simplify with a common denominator instead. - Using square brackets for infinity in interval notation . Infinity and negative infinity are not real numbers, so always close them with a round bracket, such as (-∞, 5] or [2, ∞). - Confusing the replacement set of integers with real numbers . Check whether the question specifies x ∈ N, x ∈ Z, or x ∈ R. If x is an integer, write the solution as a discrete set like {..., -1, 0, 1}, not as an interval. ## Key Links - [CBSE](https://www.swavid.com/cbse) - [Class 11](https://www.swavid.com/cbse/class-11) - [Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup) - [All 14 chapters](https://www.swavid.com/cbse/class-11/maths/chapters) - [NCERT Mathematics (Reprint 2026-27)](https://ncert.nic.in/textbook.php) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/permutations-and-combinations) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/sets) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/relations-and-functions) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/straight-lines) - [Class 11 Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup)