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4.Linear Inequalities (Graphical & Algebraic)
Class 11 • Mathematics • NCERT
Linear Inequalities (Graphical & Algebraic)
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This lesson explains linear inequalities as per NCERT Class 11. Students learn to solve inequalities algebraically and represent their solutions graphically on the number line using simple, exam-safe methods.
Lesson Objectives
- Understand the concept of linear inequalities.
- Solve linear inequalities algebraically.
- Represent solutions on the number line.
- Understand solution sets of inequalities.
1. What Is a Linear Inequality?
A linear inequality is an inequality involving a linear expression.
Examples:
x > 2
2x − 3 ≤ 5
x > 2
2x − 3 ≤ 5
2. Solving Linear Inequalities (Algebraic Method)
Linear inequalities are solved in a similar way to linear equations.
Important NCERT rule:
When both sides are multiplied or divided by a negative number, the inequality sign is reversed.
When both sides are multiplied or divided by a negative number, the inequality sign is reversed.
3. Graphical Representation on Number Line
The solution of a linear inequality can be shown on a number line.
• Open circle → < or >
• Closed circle → ≤ or ≥
• Arrow shows direction of solution
• Closed circle → ≤ or ≥
• Arrow shows direction of solution
4. Solution Set of an Inequality
The set of all real numbers that satisfy an inequality is called its solution set.
Example:
x > 2 → {x | x ∈ ℝ, x > 2}
x > 2 → {x | x ∈ ℝ, x > 2}
5. Simple NCERT Example
Solve: 2x − 3 < 5
2x < 8
x < 4
2x < 8
x < 4
Practice Questions (NCERT)
- What is a linear inequality?
- Solve: x + 3 > 7.
- Solve: 2x − 5 ≤ 1.
- What happens to the inequality sign when multiplied by −1?
- Which symbol represents “less than or equal to”?
- What does an open circle show on the number line?
- What does a closed circle show?
- Represent x ≥ 2 on the number line.
- Define solution set.
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- An inequality involving a linear expression.
- x > 4
- x ≤ 3
- The sign is reversed.
- ≤
- Strict inequality (< or >)
- Inclusive inequality (≤ or ≥)
- Closed circle at 2, arrow to the right.
- Set of values satisfying the inequality.
- Yes
© Aviate Learning – Linear Inequalities (NCERT Class 11)