Notes On Application of Simple Equations - CBSE Class 7 Maths
Solving an equation
To find the solution of an equation, a series of identical mathematical operations are performed on both the sides of the equation so that only the variable remains on one side. On simplifying all the numbers, the result obtained is the solution of the equation. If the operation is performed on only one side of the equation, the balance of the equation is disturbed.

Ex: 3x + 8 = 83
3x + 8 - 8 = 83 - 8
3x = 75
x = 75 3
x = 25.

Transposition
Moving a term of an equation from one side to the other side is called transposing. Transposing a number is same as adding to or subtracting the same number from both sides of the equation.
Ex: Solve 2x + 8 = 24
Given, 2x + 8 = 24
Transposing 8 to the right hand side, we get
⇒ 2x = 24 - 8
⇒ 2x = 16
⇒ x = 16 2
⇒ x = 8.
Hence, the value of x is 8.

The sign of a number changes when it is transposed from one side of the equation to the other. To solve puzzles/problems from practical situations equations are formed corresponding to such situations and then those equations are solved to give the solution to the puzzles/problems.

Solution to an equation
An equation can be built from the solution of the equation using the property of doing the same mathematical operation on both sides of an equation.

Summary

Solving an equation
To find the solution of an equation, a series of identical mathematical operations are performed on both the sides of the equation so that only the variable remains on one side. On simplifying all the numbers, the result obtained is the solution of the equation. If the operation is performed on only one side of the equation, the balance of the equation is disturbed.

Ex: 3x + 8 = 83
3x + 8 - 8 = 83 - 8
3x = 75
x = 75 3
x = 25.

Transposition
Moving a term of an equation from one side to the other side is called transposing. Transposing a number is same as adding to or subtracting the same number from both sides of the equation.
Ex: Solve 2x + 8 = 24
Given, 2x + 8 = 24
Transposing 8 to the right hand side, we get
⇒ 2x = 24 - 8
⇒ 2x = 16
⇒ x = 16 2
⇒ x = 8.
Hence, the value of x is 8.

The sign of a number changes when it is transposed from one side of the equation to the other. To solve puzzles/problems from practical situations equations are formed corresponding to such situations and then those equations are solved to give the solution to the puzzles/problems.

Solution to an equation
An equation can be built from the solution of the equation using the property of doing the same mathematical operation on both sides of an equation.

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