### Mathematics Class VII

Integers
Fractions and Decimals
Exponents and Powers
Algebraic Equations
Simple Linear Equations
Lines and Angles
Comparing Quantities
Congruence of Triangles
Rational Numbers
Perimeter and Area
Data Handling
Practical Geometry
Symmetry
Visualising Solid Shapes

# The Solution of an Equation

Any value of the variable which satisfies the equation is the solution of the equation.

There are two methods to solve an equation

1. By adding or subtracting the same number to both the sides of the equation as we have above seen that the equation will remain the same.

Example: 1

x + 11 = 35

Solution:

Subtract 11 from both the sides.

x + 11 – 11 = 35 – 11

x = 24

Here, x = 24 is the solution of the given equation.

Example: 2

25y = 125

Solution:

Divide both the sides by 25.

y = 5

2. Transposing Method

In this method, we transpose the numbers from one side of the equation to the other side so that all the terms with variable come on one side and all the constants come on another side.

While transposing the numbers the sign of the terms will get changed. i.e. Negative will become positive and positive will become negative.

Example

x + 11 = 35

Solution

Now we will transfer 11 from LHS to RHS and its sign will get reversed.

x = 35 – 11

x = 24

### From a Solution to the Equation

As we solve the equation to get the solution, we can get the equation also if we have the solution.

Any equation has only one solution but if we make an equation from a solution then there could be many equations.

Example

Given x = 7

3x = 21 (multiply both sides by 3)

3x + 8 = 29 (add 8 to both the sides)

This is not the only possible equation. There could be other equations also.

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