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: 6x – 3 is an expression in variable x.

Algebraic Equation

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

Example: 8x8=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.​

​​​​​​Example: The solution for the equation 2x3=5 is x=4.

More about Equations

Mathematical Operations on Expressions

  • Addition of variables: (3x+4z)+(5y+6)
  • Subtraction of variables: (4x7y)(6y+5)
  • Multiplication of variables: (5xy+6)×7x
  • Division of variables: 8xz+5z15x6y

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
2x+44=104  [Subtracting 4 from both LHS and RHS] 2x=6
2x2=62  [Dividing both LHS and RHS by 2] x=3

Methods of Solving an Equation

Method 1: 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.
Opertions involve Adding, subtracting, multipling or dividing on both sides.

Example: x+2=6
Subtract 2 from LHS and RHS
LHS: x+22=x
RHS: 62=4
But LHS = RHS
x = 4

Method 2: Transposing
It involves moving the terms to one side of the equation to find out the value of the variable.
​​​​​​​When terms move from one side to another they change their sign.
Example: x+2=6
Transpose (+2) from LHS to RHS
x=62
x=4

Applying Equations

Forming Equation from Solution

Given a solution, many equations can be constructed.

Example:  Given solution: x = 3
Multiply both sides by 4,
4x=4×3
Add -5 to both sides,
4x5=125
4x5=7
Similarly, more equations can be constructed.

 

Applications (Word problem)

Example: Ram’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 Ram’s age be x.
His father’s age is 3x.
After 15 years:
3x+15=2(x+15)
On solving,
3x+15=2x+30
3x2x=3015
x=15
Ram’s age is 15 and his dad’s age is 45.

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