Class 11 Maths Chapter 5 Linear Inequalities – Exercise 5.1 NCERT Solutions

Introduction

Exercise 5.1 introduces the concept of linear inequalities in one variable. You will learn how to solve inequalities, represent solutions on a number line, and understand the difference between equations and inequalities. This exercise builds the foundation for solving inequalities in two variables.

Key Concepts

1. Linear Inequality in One Variable: An inequality of the form

$$ax+b<0,ax+b\le 0,ax+b>0,ax+b\ge 0$$

where $a,b\in \mathbb{R},a\mathrm{\ne }0$.

2. Rules for Solving Inequalities:

   • Adding/subtracting same number on both sides does not change inequality.

   • Multiplying/dividing by positive number keeps inequality same.

   • Multiplying/dividing by negative number reverses inequality sign.

3. Representation: Solutions are represented on a number line.

NCERT Questions with Solutions (10)

Q1. Solve $2x-3>7$.

$$2x>10⟹x>5$$

Q2. Solve $3x+2\le 11$.

$$3x\le 9⟹x\le 3$$

Q3. Solve $5x-4<6$.

$$5x<10⟹x<2$$

Q4. Solve $7x+3\ge 17$.

$$7x\ge 14⟹x\ge 2$$

Q5. Solve $-2x+5>1$.

$$-2x>-4⟹x<2$$

Q6. Solve $-3x+7\le 1$.

$$-3x\le -6⟹x\ge 2$$

Q7. Solve $4x-9\ge 3$.

$$4x\ge 12⟹x\ge 3$$

Q8. Solve $6x+5<17$.

$$6x<12⟹x<2$$

Q9. Solve $-x+4\le 7$.

$$-x\le 3⟹x\ge -3$$

Q10. Solve $2x-1\ge 5$.

$$2x\ge 6⟹x\ge 3$$

FAQs (10)

1. What is linear inequality? An inequality involving linear expression.

2. What is solution of inequality? Values of variable satisfying inequality.

3. How to represent solution? On number line.

4. What happens when multiplying by negative? Inequality sign reverses.

5. What is difference between equation and inequality? Equation shows equality, inequality shows comparison.

6. Can inequality have infinite solutions? Yes, depending on range.

7. What is strict inequality? $<$ or $>$.

8. What is non‑strict inequality? $\le$ or $\ge$.

9. Can inequality solution be interval? Yes, often expressed as interval.

10. Why is this exercise important? It builds foundation for inequalities in two variables.

Conclusion

Exercise 5.1 has 10 solved questions and 10 FAQs that strengthen your understanding of linear inequalities in one variable. This builds the foundation for advanced inequality problems in Class 11 Maths.

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New Syllabus-Class 11 Maths Chapter 5 Linear Inequalities – Exercise 5.1 NCERT Solutions