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

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NCERT Solutions PDF Class 8 PDF

CBSE Class 8 Mathematics chapter, "Linear Equations in One Variable," introduces students to solving equations with a single unknown. These NCERT Solutions provide clear, step-by-step methods to master this essential algebraic concept. You'll learn how to manipulate equations using basic operations to isolate the variable, tackling everything from simple linear equations to those involving fractions and multiple steps. This practice builds a solid understanding of algebraic manipulation, which is vital for more advanced math. By working through these problems, you'll sharpen your problem-solving abilities and gain confidence in finding unknown values, setting a strong foundation for future academic success and exams.

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Quick info

BoardCBSE
ClassClass 8
Subjectगणित
Session2026
LanguageHindi
TypeNCERT Solutions
Chapter2. एक चर वाले रैखिक समीकरण

Chapter summary

Chapter 2, "Linear Equations in One Variable," focuses on understanding and solving algebraic equations that contain only one variable. The NCERT Solutions for this chapter provide clear, step-by-step methods to solve equations by performing operations on both sides to isolate the variable. It covers basic equations, fractional coefficients, and multi-step solutions, ensuring students grasp the core principles of algebraic manipulation.

Learning outcomes

  • Understand the concept of a linear equation in one variable.
  • Solve linear equations by isolating the variable.
  • Apply arithmetic operations to both sides of an equation to find the solution.
  • Solve equations involving fractions.
  • Develop algebraic problem-solving skills.

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
  • Solving Equations with Fractional Coefficients
  • Algebraic Manipulation
  • Balancing Equations

Important topics

  • Understanding Linear Equations
  • Solving Basic Linear Equations
  • Solving Equations with Fractions
  • Step-by-step Solution Methods
  • Verification of Solutions

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Questions and Solutions

2. एक चर में रैखिक समीकरण

प्रश्नावली 2.1

निम्न समीकरणों को हल कीजिए: Q1. <math>x - 2 = 7</math> हल : <math>x - 2 = 7</math> दोनों पक्षों में 2 जोड़ने पर <math>\Rightarrow</math> x - 2 + 2 = 7 + 2 ⇒ x = 9 3त्तर Q2. <math>y + 3 = 10</math> हल: <math>y + 3 = 10</math> दोनों पक्षों में से 3 घटाने पर <math>\Rightarrow</math> y + 3 - 3 = 10 - 3 <math>\Rightarrow</math> y = 7 उत्तर Q3. <math>6 = z + 2</math> हल : <math>6 = z + 2</math> दोनों पक्षों में से 2 घटाने पर <math>\Rightarrow</math> 6 - 2 = z + 2 - 2 <math>\Rightarrow</math> 4 = z <math>\Rightarrow</math> z = 4 उत्तर

Q4. <math>\frac{3}{7} + x = \frac{17}{7}</math> हल: <math display="block">\frac{3}{7} + \chi = \frac{17}{7}</math>

दोनों पक्षों में से <math>\frac{3}{7}</math> घटाने पर <math>\Rightarrow \frac{3}{7} - \frac{3}{7} + x = \frac{17}{7} - \frac{3}{7}</math> <math display="block">\Rightarrow X = \frac{17}{7} - \frac{3}{7}</math> <math display="block">\Rightarrow X = \frac{17-3}{7}</math> <math>\Rightarrow</math> x = <math>\frac{14}{7}</math> = 2 3 ca ₹ Q5. <math>6x = 12</math> हल: <math>6x = 12</math>

दोनों पक्षों में 6 से भाग देने पर

6x 12 <math>\Rightarrow \frac{}{6} = \frac{}{6}</math> <math>\Rightarrow</math> x = 2 3 c a <math>\overline{\phantom{a}}</math>

Common mistakes

  • Errors in applying operations to both sides of the equation.
  • Mistakes in handling signs when transposing terms.
  • Calculation errors with fractions.
  • Incorrectly simplifying expressions.

Revision tips

  • Review the basic properties of equality used to solve equations.
  • Practice each type of equation (addition/subtraction, multiplication/division, fractions) separately.
  • Verify your solution by substituting it back into the original equation.
  • Pay close attention to the signs of numbers when performing operations.

Practice MCQs

Q1. What is the value of x in the equation x - 2 = 7?

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

Q3. Solve for z in the equation 6 = z + 2.

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

Q5. Find the value of x in the equation 6x = 12.

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 are linear equations solved in this chapter?

Linear equations are solved by isolating the variable on one side of the equation. This is done by applying the same arithmetic operation (addition, subtraction, multiplication, or division) to both sides of the equation to maintain balance.

What is the purpose of adding or subtracting numbers from both sides of an equation?

Adding or subtracting numbers from both sides of an equation helps to move constant terms away from the variable, thereby isolating the variable and finding its value.

Why is it important to perform the same operation on both sides of an equation?

Performing the same operation on both sides ensures that the equality of the equation is maintained. It's like balancing a scale; whatever you do to one side, you must do to the other to keep it balanced.

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

To check your solution, substitute the value you found for the variable back into the original equation. If both sides of the equation are equal after substitution, your solution is correct.

Important links

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