**The vedic maths sutra to be used: "Adjust After Transposing (Paravartya Yojayet)"**

When students are introduced to the concept of solving equations, the first method taught for solving basic equations is as follows:

Let us say we want to solve the equation 3x - 9 = 0

3x - 9 = 0

3x = 9 (transposing 9 to the other side of equation)

x = 9 / 3 (adjusting 3 with 9 on the right hand side of the equation)

x = 6 (Solution of equation)

This method is little lengthy and can not be used quickly for solving complex equations. Vedic mathematics has a sutra for solving equations and is based on the same concept of transposing and then applying. (Paravartya = Transpose; Yojayet = Adjust)

So let us understand this vedic math trick to solve equations fast and easily.

There is a precondition for using this formula though, and it is that there has to be a linear relationship with ratio of coefficient of one of the unknown in the equation with the constant term. For all the linear equations satisfying this condition, can be solved by simply putting the other unknown (other than the one with ratio of coefficients in proportion of the constant) as zero.

Let us just analyse our normal method of solving equations and see how it actually gives us an answer.

Let us say, we want to solve an equation

ax + b = px + q

ax - px = q - b (transposing both the sides)

x (a - p) = q - b

x = (q - b) / (a - p) (adjusted both the sides)

Thus, every equation that we want to solve using this lengthy method, can be solved easily just by using the final solution that x = (q - b) / (a - p)

*Example 1:*

5x + 8 = 3x + 16

Without getting into any lengthy calculation, let us solve this equation by using the vedic math trick, the answer would be:

x = (16 - 8) / (5 - 3)

x = 4

*Example 2:*

4x - 6 = 3x + 16

x = (16 + 6) / (4 - 3)

x = 22

Isn't it simple solving equations using this method instead of getting into length calculations.

Now let us consider solving tricky equations with the same method.

1. Solving equations with undefined solutions

*Example 3:*

4x + 6 = 4x + 16

x = (16 - 6) / (4 - 4)

x = Undefined (This equation involved division by 0, hence the solution to this equation is undefined as it should be)

2. Solving equations expressed as ratio to one another

While solving equation expressed as ratio to one another, the solution as per vedic math trick would change a little bit as follows:

(ax + b) / (px + q) = y / z

x = (yq - zb) / (za - yp)

*Example 4:*

(3x + 5) / (6x + 4) = 7 / 8

x = (7*4 - 8*5) / (8*3 - 7*6)

x = (28 - 40) / (24 - 42)

x = (-12) / (-18)

x = 2 /3 (This solution can be checked by trying the traditional method)

Similarly, if (6x + 4) / (3x + 2) = 2, then the same vedic math trick can be used to solve this formula just by replacing 2 with (2/1) on the right hand side of the equation.

When faced with equations such as (2x + 3) / x = 13 / 5, the same vedic math trick can be used and we just need to rewrite the given equation in the format we have the solution, refer the below example.

*Example 5:*

(2x + 3) / x = 13 / 5

(2x + 3) / (1x + 0) = 13 / 5 (Rewritten the equation to match with the vedic math trick)

x = (13*0 - 5*3) / (5*2 - 13*1)

x = (0 - 15) / (10 - 13)

x = (-15) / (-3)

x = 5 (This solution can be checked by trying the traditional method)

Thus, any equation with single power of the unknown can be easily solved using this vedic math tricks. We just have to make sure to rewrite the equation in the structure provided by the vedic math trick adjust after transposing.

Solving equations is so easy ans fast with the help of vedic math tricks!

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