Solving Linear Equations with One Variable
A kid was sitting in a room with his father listening to a story.
His father said there were few soldiers on a parade ground standing in two rows in equal numbers.
He further told that
of them had started doing the parade.
And now there were total
soldiers left on the ground.
Now he asked his son if he can find the initial number of soldiers who were standing on the ground.
Let’s learn how can we find the number of soldiers.
Let’s solve this problem with the help of equations.
An equation is an algebraic expression which includes some unknown variables and constant term associated with some mathematical relations.
Few examples of equation are
Let us try to make equation for our given problem. Let us assume that
number of soldiers are standing in each row.
soldiers starts doing parade, only
were left on the ground.
We can form the equation for the above problem as
Let us solve this equation to find the no of soldiers.
is subtracted from
, so let us add
on both sides of the equation
Now, divide both side by
is multiplied with
Here we find the value of
, which is the no of soldiers in each row and also the solution of our equation.
Let’s solve one more problem for better understanding.
Suppose there were
students in your class.
Out of these,
were standing while among the rest,
students were sitting on each bench
Here we have to find total number of benches.
Now let’s make the equation and then solve for
After solving we get
, so there are total
benches in class.
Let us find the solution of algebraic expression using this equality
Suppose we have been given an algebraic equation as
from both the sides
can easily be calculated as
While solving an equation, to evaluate the constant term, we perform reverse operation by which it is associated with unknown variable on both side of equation .
But, we are not allowed to perform mathematical operation by different numbers on both the sides in an equality.
Because, it will break the equality or we can say LHS and RHS will become unequal.