# Simple Equations Class 7 Notes: Chapter 4

## Introduction to Simple Equations

### Variables and Expressions

Variable is a quantity that can take any value, its value is not fixed. It is a symbol for a number whose value is unknown yet.

Expressions are formed by performing operations like addition, subtraction, multiplication and division on the variables.

Example:Â 6x – 3 is an expression in variableÂ x.

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### Algebraic Equation

An equation is a condition on a variable such that two expressions in the variable should have equal value.

Example: 8xâˆ’8=16 is an equation.

The value of the variable in an equation for which the equation is satisfied is called the solution of the equation.â€‹

â€‹â€‹â€‹â€‹â€‹â€‹Example: The solution for the equation 2xâˆ’3=5 is x=4.
To know more about Algebraic Equation, visit here.

### Mathematical Operations on Expressions

• Subtraction of variables: (4xâˆ’7y)âˆ’(6y+5)
• Multiplication of variables: (5xy+6)Ã—7x
• Division of variables: (8xz+5z)/(5x-6y)

### Solving an Equation

Solving an equation involves performing the same operations on the expressions on either side of the “=” sign so that the value of the variable is found without disturbing the balance.
Example : Solve 2x+4=10
Consider 2x+4=10
â‡’2x+4âˆ’4=10âˆ’4Â  [Subtracting 4 from both LHS and RHS] â‡’2x=6
â‡’2x/2=6/2Â [Dividing both LHS and RHS by 2] â‡’x=3

### Methods of Solving an Equation

Method 1:Â performing the same operations on the expressions on either side of the “=” sign so that the value of the variable is found without disturbing the balance.
OpertionsÂ involveÂ Adding, subtracting, multipling or dividing on both sides.

Example: x+2=6
Subtract 2 from LHS and RHS
â‡’ LHS: x+2âˆ’2=x
â‡’ RHS: 6âˆ’2=4
But LHS =Â RHS
â‡’ x = 4

Method 2: Transposing
It involves moving the terms to one side of the equation to find out the value of the variable.
â€‹â€‹â€‹â€‹â€‹â€‹â€‹When terms move from one side to another they change their sign.
Example: x+2=6
Transpose (+2) from LHS to RHS
â‡’x=6âˆ’2
â‡’x=4

## Applying Equations

### Forming Equation from Solution

Given a solution, many equations can be constructed.

Example:Â Â Given solution: x = 3
Multiply both sides by 4,
â‡’ 4x=4Ã—3
â‡’ 4xâˆ’5=12âˆ’5
â‡’ 4xâˆ’5=7
Similarly, more equations can be constructed.

### Applications (Word problem)

Example: Ramâ€™s father is 3 times as old as his son Ram. After 15 years, he will be twice the age of his son. Form an equation and solve it.
Solution: Let Ramâ€™s age be x.
â‡’ His fatherâ€™s age is 3x.
After 15 years:
3x+15=2(x+15)
On solving,
3x+15=2x+30
3xâˆ’2x=30âˆ’15
x=15
âˆ´ Ramâ€™s age is 15 and his dadâ€™s age is 45.

## Frequently asked Questions on CBSE Class 7 Maths Notes Chapter 4: Simple Equations

### How to solve an equation?

1. Simplify each side of the equation by removing parentheses and combining like terms.
2. Use addition or subtraction to isolate the variable term on one side of the equation.
3. Use multiplication or division to solve for the variable.

### What are the different types of equation?

The different types of equations are: 1. Linear Equation.