CBSE Class 8 Maths Chapter 2: Linear Equations in One Variable NCERT Solutions

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NCERT Solutions PDF Class 8 PDF

This comprehensive set of NCERT Solutions for Class 8 Mathematics, Chapter 2, focuses on Linear Equations in One Variable. It provides clear, step-by-step explanations for solving various types of linear equations. The solutions cover fundamental concepts like isolating the variable using inverse operations such as addition, subtraction, multiplication, and division. Each problem is presented with its original question, followed by a detailed, rewritten solution that breaks down the process into manageable steps. This resource is designed to help students understand the underlying principles of solving linear equations and build confidence for their exams. It serves as an excellent tool for revision, reinforcing key algebraic skills and ensuring a solid grasp of the chapter's content.

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Quick info

BoardCBSE
ClassClass 8
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 2: Linear Equations in One Variable

Chapter summary

Chapter 2 of the Class 8 NCERT Mathematics textbook introduces the concept of Linear Equations in One Variable. This section provides detailed solutions for the exercises, guiding students through the process of solving equations by applying inverse operations to isolate the unknown variable. The solutions emphasize the systematic approach required to find the correct value of the variable, ensuring accuracy and understanding.

Learning outcomes

  • Understand the definition of a linear equation in one variable.
  • Learn to solve linear equations using basic arithmetic operations.
  • Apply inverse operations to isolate the variable.
  • Solve equations involving fractions.
  • Solve equations involving multiplication and division.
  • Develop problem-solving skills in algebra.

Topics covered

Paper topics

  • Linear Equations in One Variable
  • Solving Equations by Addition
  • Solving Equations by Subtraction
  • Solving Equations by Multiplication
  • Solving Equations by Division
  • Equations with Fractional Coefficients
  • Algebraic Manipulation
  • Variable Isolation

Important topics

  • Understanding Linear Equations in One Variable
  • Solving Equations using Inverse Operations
  • Handling Fractional Coefficients
  • Systematic Approach to Solving Equations

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Questions and Solutions

Question 1

Solve the following equation: x-2=7
Solution: To solve the equation x-2=7, we need to isolate the variable x. We can do this by performing the inverse operation of subtracting 2, which is adding 2. Add 2 to both sides of the equation:

x - 2 + 2 = 7 + 2

This simplifies to:

x = 9

Thus, the solution is x=9.

Question 2

Solve the following equation: y + 3 = 10
Solution: To solve the equation y+3=10, we need to isolate the variable y. The inverse operation of adding 3 is subtracting 3. Subtract 3 from both sides of the equation:

y + 3 - 3 = 10 - 3

This simplifies to:

y = 7

Therefore, the solution is y=7.

Question 3

Solve the following equation: 6 = z + 2
Solution: To solve the equation 6 = z + 2, we want to isolate the variable z. Since 2 is added to z, we subtract 2 from both sides of the equation:

6 - 2 = z + 2 - 2

This simplifies to:

4 = z

So, the solution is z=4.

Question 4

Solve the following equation: \frac{3}{7} + x = \frac{17}{7}
Solution: To solve the equation \frac{3}{7} + x = \frac{17}{7}, we need to isolate x. The term \frac{3}{7} is added to x, so we subtract \frac{3}{7} from both sides of the equation:

x + \frac{3}{7} - \frac{3}{7} = \frac{17}{7} - \frac{3}{7}

This simplifies to:

x = \frac{17 - 3}{7}

x = \frac{14}{7}

x = 2

The solution to the equation is x=2.

Question 5

Solve the following equation: 6x = 12
Solution: To solve the equation 6x = 12, we need to find the value of x. Since x is multiplied by 6, we perform the inverse operation, which is division. Divide both sides of the equation by 6:

\frac{6x}{6} = \frac{12}{6}

This simplifies to:

x = 2

Therefore, the solution is x=2.

Question 6

Solve the following equation: \frac{t}{5} = 10
Solution: To solve the equation \frac{t}{5} = 10, we need to isolate the variable t. Since t is divided by 5, we perform the inverse operation, which is multiplication. Multiply both sides of the equation by 5:

\frac{t}{5} \times 5 = 10 \times 5

This simplifies to:

t = 50

The solution to the equation is t=50.

Common mistakes

  • Errors in applying inverse operations (e.g., adding instead of subtracting).
  • Mistakes in fraction arithmetic when solving equations.
  • Incorrectly simplifying expressions.
  • Transposing terms without changing their signs.

Revision tips

  • Practice solving each type of equation presented in the exercise.
  • Focus on understanding why each step is taken to isolate the variable.
  • Review the rules for operating with fractions.
  • Check your answers by substituting the found value back into the original equation.

Practice MCQs

Q1. What is the first step to solve the equation x - 2 = 7?

Q2. In the equation y + 3 = 10, what is the value of y?

Q3. To solve 6 = z + 2, what operation should be applied to both sides?

Q4. What is the value of x in the equation \(\frac{3}{7} + x = \frac{17}{7}\)?

Q5. If 6x = 12, what is the value of x?

Q6. What is the solution for \(\frac{t}{5} = 10\)?

Frequently asked questions

What is a linear equation in one variable?

A linear equation in one variable is an algebraic equation that contains only one variable, and the highest power of that variable is 1. For example, x - 2 = 7 is a linear equation in one variable 'x'.

How do these NCERT solutions help Class 8 students?

These solutions provide clear, step-by-step explanations for solving linear equations, helping students understand the methods and practice them for better comprehension and exam preparation.

What are the basic operations used to solve linear equations?

The basic operations used are addition, subtraction, multiplication, and division. These are applied to both sides of the equation to isolate the variable.

How can I check if my solution to a linear equation is correct?

After finding the value of the variable, substitute it back into the original equation. If the left side equals the right side, your solution is correct.

Are equations with fractions covered in this chapter?

Yes, this chapter includes examples and exercises on solving linear equations that involve fractional coefficients.

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