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Mathematics Class 8 - Linear Equations-In-One-Variable Notes

Comprehensive study notes for Class 8 - Linear Equations-In-One-Variable olympiad preparation

Linear Equations in One Variable

Welcome to the chapter on Linear Equations in One Variable for Class 8. In this chapter, you will learn what linear equations are, how to solve them, and how to use them to solve word problems. By the end of this chapter, you will be able to solve equations and apply them in real-life situations!

Introduction

A linear equation in one variable is an equation that has only one variable and the highest power of the variable is 1. It looks like ax + b = c, where x is the variable.

Examples of Linear Equations

  • 2x + 5 = 11
  • x - 7 = 3
  • 4y = 20

Solving Linear Equations

To solve a linear equation, find the value of the variable that makes the equation true.

  • Step 1: Simplify both sides if needed.
  • Step 2: Move all variable terms to one side and constants to the other.
  • Step 3: Isolate the variable by performing operations.

Example: Solve 2x + 5 = 11
Subtract 5 from both sides: 2x = 6
Divide both sides by 2: x = 3

Applications and Word Problems

Linear equations are used to solve real-life problems. Read the problem, form an equation, and solve for the variable.

  • Example: If the sum of a number and 8 is 15, what is the number?
    Let the number be x.
    x + 8 = 15
    x = 15 - 8 = 7

Fun Activity: Equation Puzzle!

Write your own equation and ask your friends to solve it. Try using different numbers and variables!

Summary

  • A linear equation in one variable has only one variable and the highest power is 1.
  • To solve, isolate the variable using basic operations.
  • Linear equations help solve real-life problems.

Practice Questions

  1. Solve: x + 9 = 17
  2. Solve: 3y = 21
  3. Solve: 5x - 4 = 11
  4. If twice a number is 18, what is the number?
  5. Form and solve an equation: The difference between a number and 6 is 10.

Challenge Yourself

  • Create a word problem that can be solved using a linear equation in one variable.
  • Solve: 4x + 7 = 31

Did You Know?

  • Linear equations are used in science, engineering, and daily life!
  • The word "linear" comes from "line" because the graph of a linear equation is a straight line.

Glossary

  • Linear Equation: An equation with one variable and the highest power is 1.
  • Variable: A letter that stands for a number.
  • Constant: A fixed number.
  • Solution: The value of the variable that makes the equation true.

Answers to Practice Questions

  1. x = 8
  2. y = 7
  3. x = 3
  4. Number = 9
  5. x - 6 = 10 ⇒ x = 16

Practice solving linear equations to become confident in algebra!

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