All Courses
Get the App Signup / Login
Sign in Open App
Class 8 Exam  >  Class 8 Notes  >  Mathematics (Maths) Class 8  >  NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2)

NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1)

NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1)

Exercise 2.1

Q1: 3x = 2x + 18
Ans: 3x = 2x + 18
⇒ 3x – 2x = 18
⇒ x = 18
Putting the value of x in RHS and LHS, we get, 3 × 18 = (2 × 18) +18
⇒ 54 = 54
⇒ LHS = RHS


Q2: 5t – 3 = 3t – 5
Ans: 5t – 3 = 3t – 5
⇒ 5t – 3t = -5 + 3
⇒ 2t = -2
⇒ t = -1
Putting the value of t in RHS and LHS, we get, 5× (-1) – 3 = 3× (-1) – 5
⇒ -5 – 3 = -3 – 5
⇒ -8 = -8
⇒ LHS = RHS


Q3: 5x + 9 = 5 + 3x
Ans: 5x + 9 = 5 + 3x
⇒ 5x – 3x = 5 – 9
⇒ 2x = -4
⇒ x = -2
Putting the value of x in RHS and LHS, we get, 5× (-2) + 9 = 5 + 3× (-2)
⇒ -10 + 9 = 5 + (-6)
⇒ -1 = -1
⇒ LHS = RHS


Q4: 4z + 3 = 6 + 2z
Ans: 4z + 3 = 6 + 2z
⇒ 4z – 2z = 6 – 3
⇒ 2z = 3
⇒ z = 3/2
Putting the value of z in RHS and LHS, we get,
(4 × 3/2) + 3 = 6 + (2 × 3/2)
⇒ 6 + 3 = 6 + 3
⇒ 9 = 9
⇒ LHS = RHS


Q5: 2x – 1 = 14 – x
Ans: 2x – 1 = 14 – x
⇒ 2x + x = 14 + 1
⇒ 3x = 15
⇒ x = 5
Putting the value of x in RHS and LHS, we get, (2×5) – 1 = 14 – 5
⇒ 10 – 1 = 9
⇒ 9 = 9
⇒ LHS = RHS


Q6: 8x + 4 = 3 (x – 1) + 7
Ans: 8x + 4 = 3 (x – 1) + 7
⇒ 8x + 4 = 3x – 3 + 7
⇒ 8x + 4 = 3x + 4
⇒ 8x – 3x = 4 – 4
⇒ 5x = 0
⇒ x = 0
Putting the value of x in RHS and LHS, we get, (8×0) + 4 = 3 (0 – 1) + 7
⇒ 0 + 4 = 0 – 3 + 7
⇒ 4 = 4
⇒ LHS = RHS


Q7: x = 4/5 (x + 10)
Ans: x = 4/5 (x + 10)
⇒ x = 4x/5 + 40/5
⇒ x – (4x/5) = 8
⇒ (5x – 4x)/5 = 8
⇒ x = 8 × 5
⇒ x = 40
Putting the value of x in RHS and LHS, we get,
40 = 4/5 (40 + 10)
⇒ 40 = 4/5 × 50
⇒ 40 = 200/5
⇒ 40 = 40
⇒ LHS = RHS


Q8: 2x/3 + 1 = 7x/15 + 3
Ans: 2x/3 + 1 = 7x/15 + 3
⇒ 2x/3 – 7x/15 = 3 – 1
⇒ (10x – 7x)/15 = 2
⇒ 3x = 2 × 15
⇒ 3x = 30
⇒ x = 30/3
⇒ x = 10
Putting the value of x in RHS and LHS, we get,


Q9: 2y + 5/3 = 26/3 – y
Ans: 2y + 5/3 = 26/3 – y
⇒ 2y + y = 26/3 – 5/3
⇒ 3y = (26 – 5)/3
⇒ 3y = 21/3
⇒ 3y = 7
⇒ y = 7/3
Putting the value of y in RHS and LHS, we get,
⇒ (2 × 7/3) + 5/3 = 26/3 – 7/3
⇒ 14/3 + 5/3 = 26/3 – 7/3
⇒ (14 + 5)/3 = (26 – 7)/3
⇒ 19/3 = 19/3
⇒ LHS = RHS


Q10: 3m = 5m – 8/5
Ans: 3m = 5m – 8/5
⇒ 5m – 3m = 8/5
⇒ 2m = 8/5
⇒ 2m × 5 = 8
⇒ 10m = 8
⇒ m = 8/10
⇒ m = 4/5
Putting the value of m in RHS and LHS, we get,
⇒ 3 × (4/5) = (5 × 4/5) – 8/5
⇒ 12/5 = 4 – (8/5)
⇒ 12/5 = (20 – 8)/5
⇒ 12/5 = 12/5
⇒ LHS = RHS

Exercise: 2.2

Solve the following linear equations.
Q1: x/2 – 1/5 = x/3 +1/4
Ans: x/2 – 1/5 = x/3 +1/4
⇒ x/2 – x/3 =1/4+ 1/5
⇒ (3x – 2x)/6 = (5 + 4)/20
⇒ 3x – 2x = 9/20 × 6
⇒ x = 54/20
⇒ x = 27/10


Q2: n/2 – 3n/4 + 5n/6 = 21
Ans: n/2 – 3n/4 + 5n/6 = 21
⇒ (6n – 9n + 10n)/12 = 21
⇒ 7n/12 = 21
⇒ 7n = 21 × 12
⇒ n = 252/7
⇒ n = 36


Q3: x + 7 – 8x/3 = 17/6 – 5x/2
Ans: x + 7 – 8x/3 = 17/6 – 5x/2
⇒ x – 8x/3 + 5x/2 = 17/6 – 7
⇒ (6x – 16x + 15x)/6 = (17 – 42)/6
⇒ 5x/6 = – 25/6
⇒ 5x = – 25
⇒ x = – 5


Q4: (x – 5)/3 = (x – 3)/5
Ans: (x – 5)/3 = (x – 3)/5
⇒ 5(x-5) = 3(x-3)
⇒ 5x-25 = 3x-9
⇒ 5x – 3x = -9+25
⇒ 2x = 16
⇒ x = 8


Q5: (3t – 2)/4 – (2t + 3)/3 = 2/3 – t
Ans: (3t – 2)/4 – (2t + 3)/3 = 2/3 – t
⇒ ((3t – 2)/4) × 12 – ((2t + 3)/3) × 12
⇒ (3t – 2) × 3 – (2t + 3) × 4 = 2 × 4 – 12t
⇒ 9t – 6 – 8t – 12 = 8 – 12t
⇒ 9t – 6 – 8t – 12 = 8 – 12t
⇒ t – 18 = 8 – 12t
⇒ t + 12t = 8 + 18
⇒ 13t = 26
⇒ t = 2


Q6: m – (m – 1)/2 = 1 – (m – 2)/3
Ans: m – (m – 1)/2 = 1 – (m – 2)/3
⇒ m – m/2 – 1/2 = 1 – (m/3 – 2/3)
⇒ m – m/2 + 1/2 = 1 – m/3 + 2/3
⇒ m – m/2 + m/3 = 1 + 2/3 – 1/2
⇒ m/2 + m/3 = 1/2 + 2/3
⇒ (3m + 2m)/6 = (3 + 4)/6
⇒ 5m/6 = 7/6
⇒ m = 7/6 × 6/5
⇒ m = 7/5


Simplify and solve the following linear equations.
Q7: 3 (t – 3) = 5(2t + 1)
Ans: 3(t – 3) = 5(2t + 1)
⇒ 3t – 9 = 10t + 5
⇒ 3t – 10t = 5 + 9
⇒ -7t = 14
⇒ t = 14/-7
⇒ t = -2


Q8: 15(y – 4) –2(y – 9) + 5(y + 6) = 0
Ans: 15(y – 4) –2(y – 9) + 5(y + 6) = 0
⇒ 15y – 60 -2y + 18 + 5y + 30 = 0
⇒ 15y – 2y + 5y = 60 – 18 – 30
⇒ 18y = 12
⇒ y = 12/18
⇒ y = 2/3


Q9: 3 (5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
Ans: 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
⇒ 15z – 21 – 18z + 22 = 32z – 52 – 17
⇒ 15z – 18z – 32z = -52 – 17 + 21 – 22
⇒ -35z = -70
⇒ z = -70/-35
⇒ z = 2


Q10: 0.25(4f – 3) = 0.05(10f – 9)
Ans: 0.25(4f – 3) = 0.05(10f – 9)
⇒ f – 0.75 = 0.5f – 0.45
⇒ f – 0.5f = -0.45 + 0.75
⇒ 0.5f = 0.30
⇒ f = 0.30/0.5
⇒ f = 3/5
⇒ f = 0.6

The document NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1) is a part of the Class 8 Course Mathematics (Maths) Class 8.
All you need of Class 8 at this link: Class 8
79 videos|408 docs|31 tests
Join Course for Free

Top Courses for Class 8

FAQs on NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1)

1. What are linear equations in one variable?
Ans. Linear equations in one variable are mathematical expressions that can be written in the form ax + b = 0, where 'a' and 'b' are constants and 'x' is the variable. These equations represent a straight line when graphed on a coordinate plane and have a degree of 1, meaning the highest power of the variable is one.
2. How do you solve a linear equation in one variable?
Ans. To solve a linear equation in one variable, you need to isolate the variable on one side of the equation. This typically involves performing operations such as addition, subtraction, multiplication, or division on both sides of the equation until you get the variable by itself. For example, for the equation 2x + 3 = 7, you would subtract 3 from both sides to get 2x = 4, and then divide by 2 to find x = 2.
3. What is the importance of solutions to linear equations in real life?
Ans. Solutions to linear equations in real life are important because they can model various situations such as budgeting, calculating distances, and predicting profits. For instance, if a business wants to determine how many products to sell to break even, it can use a linear equation to find the necessary sales volume based on costs and revenues.
4. Can a linear equation have more than one solution?
Ans. No, a linear equation in one variable can only have one solution. This is because a straight line intersects the x-axis at only one point, which corresponds to the single value of the variable that satisfies the equation. However, if the equation is inconsistent (like 2x + 3 = 2x + 5), it has no solution.
5. What are some common mistakes to avoid when solving linear equations?
Ans. Common mistakes when solving linear equations include forgetting to apply the same operation to both sides of the equation, miscalculating arithmetic operations, and not properly isolating the variable. It is important to carefully check each step to ensure accuracy and avoid such errors.
Related Exams
About this Document
15.3K Views
4.76/5 Rating
Dec 18, 2024 Last updated
Document Description: NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation. The notes and questions for NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) have been prepared according to the Class 8 exam syllabus. Information about NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) covers topics like Exercise 2.1, Exercise: 2.2 and NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) Example, for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2).
Introduction of NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) in English is available as part of our Mathematics (Maths) Class 8 for Class 8 & NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) in Hindi for Mathematics (Maths) Class 8 course. Download more important topics related with notes, lectures and mock test series for Class 8 Exam by signing up for free. Class 8: NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1)
Description
Full syllabus notes, lecture & questions for NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1) - Class 8 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 8 | Best notes, free PDF download
Information about NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2)
In this doc you can find the meaning of NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) defined & explained in the simplest way possible. Besides explaining types of NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) theory, EduRev gives you an ample number of questions to practice NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) tests, examples and also practice Class 8 tests
79 videos|408 docs|31 tests
Join Course for Free
Download as PDF
Explore Courses for Class 8 exam

Top Courses for Class 8

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

study material

,

Objective type Questions

,

Previous Year Questions with Solutions

,

NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1)

,

MCQs

,

Viva Questions

,

practice quizzes

,

shortcuts and tricks

,

Semester Notes

,

video lectures

,

Extra Questions

,

mock tests for examination

,

Summary

,

pdf

,

Sample Paper

,

past year papers

,

Exam

,

NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1)

,

ppt

,

Important questions

,

NCERT Solutions for Class 8 Maths - Linear Equations in One Variable (Exercise 2.1)

,

Free

;
Additional Information about NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) for Class 8 Preparation

NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) Free PDF Download

The NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) is an invaluable resource that delves deep into the core of the Class 8 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) now and kickstart your journey towards success in the Class 8 exam.

Importance of NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2)

The importance of NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) cannot be overstated, especially for Class 8 aspirants. This document holds the key to success in the Class 8 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) Notes

NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2). It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) Notes on EduRev are your ultimate resource for success.

NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) Class 8 Questions

The "NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) Class 8 Questions" guide is a valuable resource for all aspiring students preparing for the Class 8 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) on the App

Students of Class 8 can study NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2), students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of NCERT Solutions: Linear Equations in One Variable(Exercise 2.1 & 2.2) is prepared as per the latest Class 8 syllabus.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup