NCERT Mathematics Class 7 - Chapter 4: Simple Equations - Notes

Learning Objectives

• Understand what an equation is and identify variables
• Solve simple linear equations
• Transpose terms in an equation
• Form equations from word problems and solve them

Key Concepts

What is an Equation?

An equation is a statement of equality containing one or more variables. Example: 2x + 3 = 7

The value of the variable that satisfies the equation is called the solution or root.

Solving Equations

Rule 1: Adding or subtracting the same number from both sides keeps the equation balanced.

Rule 2: Multiplying or dividing both sides by the same non-zero number keeps the equation balanced.

Transposition

Moving a term from one side to the other by changing its sign:

• + becomes - when transposed
• - becomes + when transposed
• × becomes ÷ when transposed
• ÷ becomes × when transposed

Example: 2x + 5 = 11 → 2x = 11 - 5 → 2x = 6 → x = 3

Forming Equations from Word Problems

Step 1: Identify the unknown and assign a variable. Step 2: Translate the problem into an equation. Step 3: Solve the equation. Step 4: Verify the solution.

Summary

Simple equations involve finding the value of an unknown variable. They are solved by performing the same operation on both sides or by transposing terms. Word problems can be converted into equations by identifying the unknown quantity.

Important Terms

Variable

A letter (like x, y, z) that represents an unknown number

Equation

A mathematical statement with an equals sign showing two expressions are equal

Solution

The value of the variable that makes the equation true

Transposition

Moving a term to the other side of the equation by reversing its operation

Quick Revision

1. An equation has an equals sign (=); an expression does not
2. Whatever you do to one side, do the same to the other side
3. Transposition changes the sign of the term
4. Always verify your answer by substituting back
5. LHS = RHS must hold true for the correct solution

Practice Tips

• Start with simple equations and gradually increase difficulty
• Create your own word problems and convert them to equations
• Always check your answer by substituting it back into the original equation