SIMPLE EQUATION : How to find an unknown number by balancing method & transposing method?

UTPAL SHARMA

INTRODUCTION:-

As per the title, we will understand the simple equation. Yes, the first question arising what is the equation or simple equation?

We may say that when an expression has an equal sign then the expression is known as Equation or simple equation.

The equation may be numerical. But here we will discuss a linear equation with one variable.


Terminology:-

Variable

An alphabet is used other than numbers present in the equation. Example - a, b, x, y, z, etc.


Constant

The number is used other than a variable in an equation. Example - 1, 2, 3, 11, 30 etc.

SIMPLE EQUATION-How to find an unknown number by balancing method & transposing method?


Before go ahead read the picture for better understanding.....


L.H.S.

It is a Left-hand side of any equation.


R.H.S.

It is a Right-hand side of any equation.

Simple Equation

When we need to find an unknown number in any given situation then we use a simple equation. 

In some conditions, a simple equation is given & we need to find an unknown number.

Let's discuss -

You remember in your childhood, your friend asked you about Mind reading game -
  1. He said to you......Think a number.
  2. OK now double the number.
  3. Add four in your answer.
  4. Now tell me the total sum, I will tell you which number you were thinking. 
After all, he tells you the answer & you were thinking about how it is work. So now we will understand it. 

First, suppose your total sum is 30.
  1. Suppose I am your friend & I don't know which number you were thinking. So I consider it x.
  2.  Now double it 2x.
  3. Add four in it 2x+4.
  4. Its total sum equal to 2x+4=30
Here we get a simple equation 2x+4=30 & we will find unknown number x. 


How to find the unknown number?

Here we have three methods for finding an unknown number -
  • Trial & error method
  • Balanced method
  • Transposing method 
We will discuss the two most useful methods for finding an unknown number -


Balanced method

As per its name, we will balance the equation & find the unknown number. Take the above simple equation for finding an unknown number x.
  • 2x+4=30 
(For remove +4 we use opposite sign & we will need -4 so we will take -4 in L.H.S. & R.H.S. for balancing)
  • 2x+4-4=30-4
  • 2x=26 
(Now we need to remove 2, here 2 is in multiply So we take its opposite sign & we will divide by 2 in L.H.S. & R.H.S.)
  • (2x÷2)=(26÷2)
  • x=13
Here we get our unknown number x=13. Now discuss the second method.


Transposing Method

In the transposing method, we will transpose the number. Let's discuss in simple equation 2x+4=30.
  • 2x+4=30
(First, we will transpose +4 from L.H.S. to R.H.S. but it will change their sign)
  • 2x=30-4
  • 2x=26
( Now, here 2 is in multiply so we will send it in the divide of R.H.S.)
  • x=(26÷2)
  • x=13
Here we get unknown number x=13.


Conclusion

Finally, we get an unknown number with the help of the balancing method & transposing method. Transposing method is a very useful & easy method as compared to others. It is used in higher classes in mathematics expressions.
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