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.

After 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.

Here is subtracted from , so let us add on both sides of the equation

Now, divide both side by since is multiplied with

Here we find the value of as , 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 as , 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

we subtract from both the sides

Hence, 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.

The End