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Linear Inequalities — Flashcards

Punjab Board · Class 11 · Mathematics

25 flashcards for Linear Inequalities (Punjab Board Class 11 Mathematics) to test yourself on key terms and facts.

45 questions25 flashcards2 formulas & key relations5 concepts

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An infographic classifying different types of inequalities based on variables, symbols, and degree, including numerical, literal, strict, slack, linear in one variable, linear in two variables, and qu
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25 Flashcards·
Linear inequalities in one variableDouble inequalitiesGraphical representation and interval notation
Card 1Linear inequalities in one variable

Solve: 5x + 3 < 18. What is the solution?

Answer

Step 1: Subtract 3 from both sides → 5x < 15 Step 2: Divide both sides by 5 → x < 3 Answer: x < 3, or x ∈ (-∞, 3) Key point: When dividing by a positive number, the inequality sign stays the same.

Card 2Linear inequalities in one variable

Solve: -3x + 7 ≥ 1. Show step-by-step work.

Answer

Step 1: Subtract 7 from both sides → -3x ≥ -6 Step 2: Divide both sides by -3. Since we divide by a NEGATIVE number, REVERSE the inequality sign → x ≤ 2 Answer: x ≤ 2, or x ∈ (-∞, 2] Critical rule: A…

Card 3Linear inequalities in one variable

When do you REVERSE the inequality sign? Give an example.

Answer

You reverse the inequality sign ONLY when: 1. Multiplying both sides by a negative number 2. Dividing both sides by a negative number Example: -2x > 8 Step 1: Divide by -2 (negative!) → x < -4 (sign …

Card 4Linear inequalities in one variable

Solve: 7x - 5 > 2x + 10

Answer

Step 1: Subtract 2x from both sides → 5x - 5 > 10 Step 2: Add 5 to both sides → 5x > 15 Step 3: Divide by 5 (positive number) → x > 3 Answer: x > 3, or x ∈ (3, ∞) Graphical representation: Open circl…

Card 5Linear inequalities in one variable

Solve: (5x - 2)/3 ≤ (x + 4)/2

Answer

Step 1: Multiply both sides by 6 (LCM of 3 and 2) → 2(5x - 2) ≤ 3(x + 4) Step 2: Expand → 10x - 4 ≤ 3x + 12 Step 3: Subtract 3x from both sides → 7x - 4 ≤ 12 Step 4: Add 4 to both sides → 7x ≤ 16 Step…

Card 6Double inequalities

Solve the compound inequality: 2 ≤ 3x - 1 < 8

Answer

This means: 2 ≤ 3x - 1 AND 3x - 1 < 8 For the left part: 2 ≤ 3x - 1 Step 1: Add 1 to both sides → 3 ≤ 3x Step 2: Divide by 3 → 1 ≤ x (or x ≥ 1) For the right part: 3x - 1 < 8 Step 1: Add 1 to both s…

Card 7Double inequalities

Solve: -5 ≤ (3 - 2x)/4 ≤ 1

Answer

Step 1: Multiply all parts by 4 → -20 ≤ 3 - 2x ≤ 4 For the left part: -20 ≤ 3 - 2x Step 2a: Subtract 3 from both sides → -23 ≤ -2x Step 3a: Divide by -2 (negative!), reverse signs → 23/2 ≥ x (or x ≤ …

Card 8Graphical representation and interval notation

What is the difference between 'x < 5' and 'x ≤ 5' on a number line?

Answer

'x < 5' (strict inequality): - Represented by an OPEN circle at 5 - Does NOT include 5 itself - All numbers less than 5 - Interval notation: (-∞, 5) 'x ≤ 5' (slack inequality): - Represented by a CLO…

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Frequently Asked Questions

What are the important topics in Linear Inequalities for Punjab Board Class 11 Mathematics?
Key topics in Linear Inequalities include Basic Concepts and Definitions, Rules for Solving Linear Inequalities, Solving Linear Inequalities in One Variable — Step-by-Step Methods, Worked Examples — One Variable Inequalities. Study these first, then practise questions on each for Class 11 exams.
How many flashcards are available for Linear Inequalities?
There are 25 flashcards for Linear Inequalities covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Linear Inequalities for Class 11 exams?
Learn the core ideas first, then work through the 45 practice questions on Linear Inequalities. Revise definitions regularly and use flashcards for quick recall before the exam.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Punjab Board Class 11 Mathematics Flashcards

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