CLASS-6
RULES OF TRANSPOSITION

RULES OF TRANSPOSITION -

The "rule of transposition" is not a commonly used term in mathematics, but it might be referring to the concept of transposition in the context of equations. Transposition is a fundamental technique used in algebra to manipulate equations and move terms from one side of an equation to the other side while preserving equality.

Here's how the rule of transposition works:-

Suppose you have an equation of the form ax + b = c, and you want to isolate the variable x. To do this, you can use the rule of transposition, which involves the following steps:

  1. Start with the original equation:-ax + b = c.
  2. To isolate x, move the term containing b to the other side of the equation:- Subtract b from both sides of the equation. This step is sometimes called "transposing" or "moving terms."Original equation: ax + b = c .  After transposition: ax = c − b
  3. Now, the variable x is isolated on the left side of the equation:-  To find the value of x\, divide both sides of the equation by the coefficient \(a:x = (c − b)/a. ​The result is an equation where x is isolated on one side, and you can easily solve for the value of x. So, in summary, the rule of transposition involves changing the position of terms in an equation while maintaining equality, and it's commonly used when solving linear equations to isolate variables.


The rule of transposition, also known as "moving terms" or "changing sides," is a fundamental concept in algebra that allows you to change the position of terms in an equation while maintaining equality. This is particularly useful when isolating variables in equations. Let's look at an example:-

Example:-

Suppose you have the following equation and you want to isolate the variable x:

        3x + 7 = 22

To do this, you can use the rule of transposition, which involves changing the position of the terms to isolate x:

  1. Start with the original equation: 3x + 7 = 22
  2. Move the constant term (7) to the other side of the equation by subtracting it from both sides. This step is known as transposition: 

              3x = 22 − 7

  1. Now, the variable x is isolated on the left side of the equation:- 3x = 15
  2. To solve for x, divide both sides by the coefficient 3: 3x = 15​
  3. Simplify the right side: x = 5

So, the solution to the equation is x = 5. You've isolated the variable x by using the rule of transposition to move the constant term to the other side of the equation.