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Mathematics Class 7 - Simple Linear-Equations Notes

Comprehensive study notes for Class 7 - Simple Linear-Equations olympiad preparation

Simple Linear Equations

Welcome to the chapter on Simple Linear Equations for Class 7. In this chapter, you will learn what linear equations are, how to solve them, and how they are used in real life. By the end of this chapter, you will be able to solve simple equations and use them to solve word problems!

Introduction

A linear equation is an equation where the highest power of the variable is 1. It helps us find unknown values by balancing both sides of the equation.

What is a Simple Linear Equation?

A simple linear equation looks like ax + b = c, where x is the variable, and a, b, and c are numbers.

  • Example: 2x + 3 = 11
  • Example: x - 5 = 7

How to Solve a Simple Linear Equation?

  • Step 1: Move all numbers to one side and the variable to the other side.
  • Step 2: Use addition, subtraction, multiplication, or division to find the value of the variable.

Example 1: x + 4 = 10
Subtract 4 from both sides: x = 10 - 4 = 6

Example 2: 3x = 15
Divide both sides by 3: x = 15 ÷ 3 = 5

Word Problems Using Linear Equations

Sometimes, you need to form an equation from a word problem and solve it.

  • Example: Riya has some pencils. If she buys 5 more, she will have 12. How many pencils does she have now?
    Let the number of pencils be x.
    x + 5 = 12
    x = 12 - 5 = 7

Fun Activity: Equation Hunt!

Write down three equations using your age, your friend's age, and the number of books you have. Solve them and check your answers!

Summary

  • A linear equation has the variable to the power of 1.
  • Solve equations by balancing both sides.
  • Use equations to solve word problems.

Practice Questions

  1. Solve: x + 7 = 15
  2. Solve: 4x = 20
  3. Solve: x - 3 = 9
  4. If 2x + 5 = 13, what is x?
  5. Form an equation: The sum of a number and 8 is 14. Find the number.

Challenge Yourself

  • Solve: 5x - 10 = 15
  • A number multiplied by 6 gives 42. What is the number?

Did You Know?

  • Linear equations are used in science, engineering, and daily life!
  • Solving equations helps you think logically and solve problems faster.

Glossary

  • Equation: A statement that two things are equal.
  • Variable: A letter that stands for a number.
  • Linear: Highest power of the variable is 1.

Answers to Practice Questions

  1. x = 8
  2. x = 5
  3. x = 12
  4. 2x + 5 = 13 → 2x = 8 → x = 4
  5. x + 8 = 14 → x = 6

Practice solving simple linear equations to become a math expert!

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