Almost all the chapters that we have discussed till now have dealt with the arithmetical part of Vedic Mathematics. In this chapter, we will study the algebraic part of this science.

In Vedic Mathematics there are many simple formulae for solving different types of equations. Each such formula can be used for a particular category of equations. Let us assume that we have to solve an equation of the type ax + b = cx + d. Then the answer to this equation can be easily determined using the formula.

The question asks us to solve the equation 4x + 7 = 5x + 3. The equation is of the type ax + b = cx + d where the values of a, b, c and d are 5, 3, 4 and 7 respectively. The value of x 146 VEDIC MATHEMATICS MADE EASY

**Can be solved by using the simple formula as given below:**

x = d – b

a – c

**(Q) Solve the equation 5x + 3 = 6x – 2.**

We represent the equation in the form of ax + b = cx + d and get the values of a, b, c and d as 5, 3, 6 and -2 respectively. The value of x is

Thus we get a simple rule that equations of the type ax + b = cx + d can be solved using the formula x = d – b

a-c

**METHOD TWO**

The method given above was the simplest method of solving equations. Now we come to another method. This particular method is used to solve equations of the type (x + a) (x + b) = (x + c) (x + d). The value of x will be found using the formula

x = cd – ab

a + b – c – d

**Q. Solve the equation (x + 1) (x + 3) = (x – 3) (x – 5).**

The above equation is of the type (x + a) (x + b) = (x + c) (x + d). Thus the numbers 1, 3, -3 and -5 are represented by the letters a, b, c and d respectively. The value of x will be

GENERAL EQUATIONS 147

**(Q) Solve the equation (x + 7) (x + 12) = (x + 6) (x + 15).**

We represent the numbers 7, 12, 6 and 5 with the letters a, b, c and d respectively. The value of x will be

It can be inferred from the above examples that the value of the equation (x + a) (x + b) = (x + c) (x + d) can be easily determined using the principles of Vedic Mathematics.

**We can tabulate our findings as follows:**