Solving linear equation of the form ax+b=c

 Sankalana-vyavakalanabhyam" is another Vedic Mathematics sutra that deals with solving linear equations. The phrase can be translated as "By addition and by subtraction."

This sutra is used to solve equations of the form ax + b = c or ax - b = c, where 'a,' 'b,' and 'c' are constants, and 'x' is the variable you need to find.

The process involves two steps:

Sankalana (Addition):

If the equation is of the form ax + b = c, the first step is to isolate the variable term (ax) on one side of the equation. To do this, you subtract 'b' from both sides of the equation.

For example, if you have the equation 3x + 5 = 14, you perform the following steps:

3x + 5 - 5 = 14 - 5

3x = 9

Vyavakalana (Subtraction):

In the second step, you isolate the variable (x) by dividing both sides of the equation by the coefficient of the variable (in this case, 'a').F

or the example above, you divide both sides by 3:

(3x)/3 = 9/3

x = 3

So, the solution to the equation 3x + 5 = 14 is x = 3.

Similarly, if the equation is of the form ax - b = c, you follow the same steps, but this time, you add 'b' to both sides in the first step:

For example, if you have the equation 4x - 7 = 17, you perform the following steps:

4x - 7 + 7 = 17 + 7

4x = 24

x = 6

By using the "Sankalana-vyavakalanabhyam" technique, you can efficiently solve linear equations and find the value of the variable 'x' in a relatively straightforward manner.

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