Checking for Solutions of Equation
Suppose, you want to check the mileage of your new car.
So, you filled
$8$
liters of petrol in your car.
You travel
$40$
km by your car and the fuel gets completely exhausted.
This situation can be presented as
This equation is a condition on the variable
$x$
If we can calculate value of variable
$x$
, we get the mileage of the car
Hence, we need to find out the solution of the equation.
Letâ€™s try to find out the solution of an equation.
First, we write the equation as such
The value of the variable which satisfies the equation is called as the solution to the equation.
So, we start to put the values of variable
$x$
as
$x=1,2,3,4$
But, no value of variable
$x$
satisfies the equation
When, we put the value of variable as
$x=5$
, it satisfies the equation
Hence,
$x=5$
is the solution to the equation
Here, this method is called as trial method to find out the solution of the equation.
Because, we get the solution in five consecutive trials as
$x=1,2,3,4,5$
.
Now, let us learn the practical method of solution to the equation.
Letâ€™s see the practical method of solution to the equation.
We know that the sign of equality always occurs in the equation.
Hence, we can perform same arithmetic operation to both the sides as
$L.H.S.$
as well as
$R.H.S.$
.
We have the equation
So, we divide both the sides by
$8$
to free the variable in
$L.H.S.$
.
On further simplification, we get the value of variable as
Thus, we conclude that the value of the variable which satisfies the equation is called as the solution to the equation.
Revision
The value of the variable in the equation which satisfies the equation is called as the solution to the equation.
The solution to the equation can be found out by using trial method or practical method.
The End