Class 10 Maths Chapter 3 Exercise 3.2 Solution provides step-by-step solutions and detailed explanations to help students understand the concepts easily and effectively.
Class 10 Maths Chapter 3 Exercise 3.2 Solutions – Questions and Answers
Here is a comprehensive list of questions and answers for Class 10 Maths Chapter 3 Exercise 3.2. These solutions will help you understand the topic and prepare for your exams. Let's go through some of the important questions and their answers.
Questions and Answers
Question 1:
Find the value of x in the equation 2x + 5 = 15.
Answer:
To solve for x, subtract 5 from both sides to get 2x = 10. Now divide by 2 to find x = 5.
Question 2:
Simplify the expression 3(x + 4) - 2x.
Answer:
First, distribute 3 across the parentheses to get 3x + 12. Now, subtract 2x from 3x to get x + 12 as the final simplified expression.
Question 3:
Solve for y in the equation 5y - 3 = 2y + 12.
Answer:
Subtract 2y from both sides to get 3y - 3 = 12. Then, add 3 to both sides to get 3y = 15. Finally, divide by 3 to find y = 5.
Question 4:
Find the value of p if 4p - 7 = 9.
Answer:
Add 7 to both sides to get 4p = 16. Now divide by 4 to find p = 4.
Question 5:
What is the value of x in the equation 3x/4 = 9?
Answer:
Multiply both sides of the equation by 4 to get 3x = 36. Then, divide by 3 to find x = 12.
Question 6:
Solve for a in the equation 2a + 8 = 18.
Answer:
Subtract 8 from both sides to get 2a = 10. Now divide by 2 to find a = 5.
Question 7:
Find the value of y if 6y + 3 = 21.
Answer:
Subtract 3 from both sides to get 6y = 18. Now, divide by 6 to find y = 3.
Question 8:
Solve the equation 5(x - 2) = 3x + 4.
Answer:
First, distribute 5 across the parentheses to get 5x - 10 = 3x + 4. Now, subtract 3x from both sides to get 2x - 10 = 4. Then add 10 to both sides to get 2x = 14. Finally, divide by 2 to find x = 7.
Question 9:
Find the value of z in the equation 7z - 2 = 5z + 8.
Answer:
Subtract 5z from both sides to get 2z - 2 = 8. Now, add 2 to both sides to get 2z = 10. Finally, divide by 2 to find z = 5.
Question 10:
Solve for m if 3m + 5 = 2m + 8.
Answer:
Subtract 2m from both sides to get m + 5 = 8. Now subtract 5 from both sides to get m = 3.
Question 11:
Find the value of x in the equation 4x + 10 = 18.
Answer:
Subtract 10 from both sides to get 4x = 8. Now divide by 4 to find x = 2.
Question 12:
Simplify the expression 2(3x - 4) + 5x.
Answer:
Distribute 2 across the parentheses to get 6x - 8. Then, add 5x to 6x to get 11x - 8 as the final simplified expression.
Question 13:
Solve for p if 9p - 7 = 20.
Answer:
Add 7 to both sides to get 9p = 27. Now divide by 9 to find p = 3.
Question 14:
What is the value of x in the equation 5x + 4 = 29?
Answer:
Subtract 4 from both sides to get 5x = 25. Now divide by 5 to find x = 5.
Question 15:
Solve the equation 8y - 4 = 2y + 12.
Answer:
Subtract 2y from both sides to get 6y - 4 = 12. Now add 4 to both sides to get 6y = 16. Finally, divide by 6 to find y = 8/3.
Question 16:
Find the value of x in the equation x/3 = 7.
Answer:
Multiply both sides by 3 to get x = 21.
Question 17:
Solve for t in the equation 6t + 2 = 5t + 12.
Answer:
Subtract 5t from both sides to get t + 2 = 12. Now subtract 2 from both sides to get t = 10.
Question 18:
Find the value of m in the equation 3m - 2 = 7.
Answer:
Add 2 to both sides to get 3m = 9. Now divide by 3 to find m = 3.
Question 19:
Simplify the expression 4(2x - 1) + 3x.
Answer:
Distribute 4 across the parentheses to get 8x - 4. Then, add 3x to 8x to get 11x - 4 as the final simplified expression.
Question 20:
Solve for y if 2y + 6 = 3y - 4.
Answer:
Subtract 2y from both sides to get 6 = y - 4. Now add 4 to both sides to get y = 10.
Additional Questions for Further Practice:
Question 21:
Find the value of x in the equation 3x + 7 = 19.
Answer:
Subtract 7 from both sides to get 3x = 12. Now divide by 3 to find x = 4.
Question 22:
Solve for z in the equation 5z - 8 = 2z + 10.
Answer:
Subtract 2z from both sides to get 3z - 8 = 10. Now add 8 to both sides to get 3z = 18. Finally, divide by 3 to find z = 6.
Question 23:
Find the value of y in the equation 2y + 4 = 10.
Answer:
Subtract 4 from both sides to get 2y = 6. Now divide by 2 to find y = 3.
Question 24:
Simplify the expression 7(3x + 2) - 4x.
Answer:
Distribute 7 across the parentheses to get 21x + 14. Then, subtract 4x from 21x to get 17x + 14 as the final simplified expression.
Question 25:
Solve for a in the equation 4a + 6 = 18.
Answer:
Subtract 6 from both sides to get 4a = 12. Now divide by 4 to find a = 3.
Question 26:
Solve for n in the equation 2n - 5 = 15.
Answer:
Add 5 to both sides to get 2n = 20. Now divide by 2 to find n = 10.
Question 27:
Find the value of x in the equation 5x + 2 = 7x - 4.
Answer:
Subtract 5x from both sides to get 2 = 2x - 4. Now add 4 to both sides to get 6 = 2x. Finally, divide by 2 to find x = 3.
Question 28:
Solve for m in the equation 3m + 5 = 14.
Answer:
Subtract 5 from both sides to get 3m = 9. Now divide by 3 to find m = 3.
Question 29:
Find the value of y in the equation 4y - 1 = 7.
Answer:
Add 1 to both sides to get 4y = 8. Now divide by 4 to find y = 2.
Question 30:
Simplify the expression 5(2x + 3) + 7x.
Answer:
Distribute 5 across the parentheses to get 10x + 15. Then, add 7x to 10x to get 17x + 15 as the final simplified expression.
Question 31:
Solve for p in the equation 3p - 4 = 8.
Answer:
Add 4 to both sides to get 3p = 12. Now divide by 3 to find p = 4.
Question 32:
What is the value of x in the equation 2x - 6 = 10?
Answer:
Add 6 to both sides to get 2x = 16. Now divide by 2 to find x = 8.
Question 33:
Solve for z in the equation 7z - 4 = 18.
Answer:
Add 4 to both sides to get 7z = 22. Now divide by 7 to find z = 22/7.
Question 34:
Find the value of y in the equation 3y + 5 = 14.
Answer:
Subtract 5 from both sides to get 3y = 9. Now divide by 3 to find y = 3.
Question 35:
Simplify the expression 4(3x - 5) + 2x.
Answer:
Distribute 4 across the parentheses to get 12x - 20. Then, add 2x to 12x to get 14x - 20 as the final simplified expression.
Question 36:
Solve for x in the equation 4x + 7 = 19.
Answer:
Subtract 7 from both sides to get 4x = 12. Now divide by 4 to find x = 3.
Question 37:
Find the value of m in the equation 3m + 6 = 12.
Answer:
Subtract 6 from both sides to get 3m = 6. Now divide by 3 to find m = 2.
Question 38:
Simplify the expression 3(2x - 1) + 5x.
Answer:
Distribute 3 across the parentheses to get 6x - 3. Then, add 5x to 6x to get 11x - 3 as the final simplified expression.
Question 39:
Solve for a in the equation 2a + 3 = 11.
Answer:
Subtract 3 from both sides to get 2a = 8. Now divide by 2 to find a = 4.
Question 40:
Find the value of z in the equation 5z - 8 = 22.
Answer:
Add 8 to both sides to get 5z = 30. Now divide by 5 to find z = 6.
Question 41:
Solve for b in the equation 2b + 6 = 16.
Answer:
Subtract 6 from both sides to get 2b = 10. Now divide by 2 to find b = 5.
Question 42:
Simplify the expression 5(2x - 1) + 3x.
Answer:
Distribute 5 across the parentheses to get 10x - 5. Then, add 3x to 10x to get 13x - 5 as the final simplified expression.
Question 43:
Solve for t in the equation 3t + 4 = 16.
Answer:
Subtract 4 from both sides to get 3t = 12. Now divide by 3 to find t = 4.
Question 44:
Find the value of x in the equation 6x + 3 = 15.
Answer:
Subtract 3 from both sides to get 6x = 12. Now divide by 6 to find x = 2.
Question 45:
Solve for r in the equation 5r - 4 = 16.
Answer:
Add 4 to both sides to get 5r = 20. Now divide by 5 to find r = 4.
Question 46:
Find the value of y in the equation 2y + 5 = 11.
Answer:
Subtract 5 from both sides to get 2y = 6. Now divide by 2 to find y = 3.
Question 47:
Simplify the expression 3(4x - 2) + 5x.
Answer:
Distribute 3 across the parentheses to get 12x - 6. Then, add 5x to 12x to get 17x - 6 as the final simplified expression.
Question 48:
Solve for a in the equation 6a - 8 = 16.
Answer:
Add 8 to both sides to get 6a = 24. Now divide by 6 to find a = 4.
Question 49:
Find the value of b in the equation 5b + 4 = 24.
Answer:
Subtract 4 from both sides to get 5b = 20. Now divide by 5 to find b = 4.
Question 50:
Solve for x in the equation 7x - 3 = 11.
Answer:
Add 3 to both sides to get 7x = 14. Now divide by 7 to find x = 2.
These questions and answers should help you practice and master Class 10 Maths Chapter 3 Exercise 3.2.
Best Indian Books for Class 10 Maths Chapter 3 Exercise 3.2 Solution
Mathematics for Class 10 by R.D. Sharma
Publication: Dhanpat Rai Publications
Content: This book provides a detailed explanation of various mathematical concepts, including algebraic identities and linear equations. It includes numerous examples and exercises that help students understand the application of formulas and improve problem-solving skills. The questions are arranged by difficulty, ensuring a gradual learning curve.
NCERT Mathematics for Class 10
Publication: National Council of Educational Research and Training (NCERT)
Content: NCERT books are highly recommended for Class 10 students. The exercises are designed to build foundational skills, with clear explanations of theorems and definitions. Chapter 3 focuses on pairs of linear equations and provides problems that challenge students to apply algebraic methods to solve real-life situations.
Understanding Mathematics - Class 10 by M.L. Agarwal
Publication: Sultan Chand & Sons
Content: M.L. Agarwal’s book is known for its conceptual clarity and variety of questions. Chapter 3 contains well-structured exercises that include both solved and unsolved problems. The solutions help reinforce understanding through step-by-step problem-solving techniques.
Lab Manual Mathematics Class 10 by G. R. Puri
Publication: Goyal Publishers
Content: This manual provides a hands-on approach to understanding mathematics with practical applications. It includes experiments and real-time problem-solving, particularly focusing on the practical aspects of Chapter 3 on algebra.
Objective Mathematics for Class 10 by R.S. Aggarwal
Publication: S. Chand & Company
Content: R.S. Aggarwal’s book is designed for students looking for more practice in objective-type questions. This book is a great resource for mastering the concepts in Chapter 3 and offers ample exercises to practice various types of questions, including multiple-choice and assertion-reasoning type.
Mathematics Class 10 by T.K. Soni
Publication: R.K. Publishers
Content: This book focuses on developing a deep understanding of the subject by providing a wide range of examples and problems. The exercises in Chapter 3 cover different aspects of linear equations, ensuring that students can master both easy and complex questions.
S. K. Gupta Mathematics for Class 10
Publication: Arihant Publications
Content: This book is known for its clear explanations and diverse set of problems. It contains detailed solutions to all types of questions, from simple to challenging, helping students of different learning speeds master the concepts in Chapter 3 effectively.
Foundation Course in Mathematics - Class 10 by M.S. Chouhan
Publication: Vikas Publications
Content: M.S. Chouhan’s book is well-suited for students seeking both theory and application-based exercises. Chapter 3 covers exercises that focus on linear equations, with a mix of solved examples and practice problems to help students hone their skills.
Mathematics for Class 10 by S.K. Das
Publication: Arihant Publications
Content: S.K. Das provides an in-depth approach to each topic, with exercises that build on the basic concepts covered in class. This book is a great companion for students who need to practice and reinforce the lessons learned in Chapter 3.
Mathematics Class 10 by J. Sharma
Publication: Pearson India
Content: This book contains a rich variety of questions that cater to the understanding of concepts in linear equations. The exercises in Chapter 3 offer problems that require critical thinking and application of algebraic methods to find solutions.
New Mathematics Today for Class 10 by Dr. S.K. Gupta
Publication: New Saraswati House
Content: A very useful book for students preparing for board exams, this book offers comprehensive explanations and practical examples. The exercises focus on building a strong foundation in algebra and solving linear equations.
All-in-One Mathematics for Class 10 by Arihant Experts
Publication: Arihant Publications
Content: This book provides a consolidated approach for all topics of Class 10, including Chapter 3. It contains solved examples, practice problems, and previous years' question papers for better preparation.
Mathematics Class 10 by K.K. Arora
Publication: Indra Prakashan
Content: K.K. Arora’s book is excellent for students looking for extra practice. The exercises in Chapter 3 are thoughtfully designed to improve algebraic skills, and the solutions offer detailed explanations of how to approach each type of problem.
Mathematics for Class 10 by R.K. Bansal
Publication: Bansal Publishers
Content: Known for its precise and concise approach, this book offers a variety of questions to test the understanding of algebraic methods. Chapter 3 provides both basic and advanced level exercises on linear equations.
Mathematics for Class 10 by N. K. Soni
Publication: Goyal Publishers
Content: This book is helpful for students who wish to learn through practical applications of mathematics. The exercises in Chapter 3 provide an excellent blend of theory and problem-solving methods to ensure complete understanding.
The Magic of Mathematics - Class 10 by T.S. Kamaraj
Publication: Kamaraj Publications
Content: T.S. Kamaraj’s book offers a fresh approach to mathematics by providing easy-to-understand language and a clear presentation of concepts. The exercises in Chapter 3 are filled with application-based questions that require in-depth learning and practice.
Mathematics Class 10 by R.B. Sharma
Publication: Goyal Publishers
Content: R.B. Sharma’s book focuses on both the theory and practice of algebra. The problems in Chapter 3 cover linear equations and offer a variety of scenarios where these equations are used to solve real-world problems.
Comprehensive Mathematics for Class 10 by J.B. Gupta
Publication: Laxmi Publications
Content: This book is a great resource for students aiming for high scores in their exams. It contains exercises on linear equations with varied difficulty levels to cater to different learning needs.
ICSE Mathematics for Class 10 by Dr. R.S. Aggarwal
Publication: S. Chand & Company
Content: This book is tailored to the ICSE curriculum but is also helpful for CBSE students. It provides a broad range of questions in Chapter 3, enabling students to apply their algebraic skills.
Mathematics Class 10 by R. C. Soni
Publication: Vikas Publishers
Content: This book provides step-by-step solutions for each problem in Chapter 3, with a focus on building confidence in solving algebraic equations. It also includes practice problems that align well with board exam patterns.
Class 10 Maths Chapter 3 Exercise 3.2 Solution
Class 10 Maths Chapter 3 Exercise 3.2 focuses primarily on solving linear equations in two variables. These types of equations are fundamental in algebra, providing students with the tools to approach real-world problems involving relationships between two unknowns. Linear equations represent straight lines when plotted on a graph, and solving them means finding the point where the lines intersect.
This exercise primarily deals with methods of solving such equations, including substitution, elimination, and graphical methods. Students are tasked with finding the values of the variables that satisfy the given equations. The solutions are often based on algebraic manipulation, where one equation is substituted into another or variables are eliminated to isolate one variable and solve for it.
Each question in the exercise encourages students to break down the equations step by step. The exercises cover a range of problems, from simple direct calculations to word problems that require translating real-world situations into algebraic expressions. This helps students not only practice their algebra skills but also improve their logical thinking and problem-solving abilities.
A key aspect of solving these exercises is understanding the concept of balance in equations. Students learn that whatever operation is performed on one side of the equation must also be performed on the other side. This principle is fundamental to the integrity of algebraic solutions.
Moreover, the exercises also include some applications, such as determining the values of two quantities based on their relationships, which reinforces the practical importance of solving linear equations. By the end of this chapter, students should be able to approach complex algebraic problems confidently, making it an essential foundation for further studies in mathematics.
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