Transformation of Equations and Formulas

Equality of Members

The main characteristic of an equation is that it contains two members which are equal to each other. Their quality is indicated by the equals sign between the members. Each member may consist of one or more terms, numeral or literal. For example: 8 ─ 3 = 5; a + b = c + d

Whatever operations are performed to change the form of an equation, the equality of the two sides, or members, of the equation must be preserved. Equations are a valuable tool for finding unknown values in innumerable applications, but they are valid only if, at any point in the calculations, the left side equals the right side of the equation. The members themselves may change, the individual terms may be moved from one side of the equation to the other, but the equality of both sides must be maintained.

An equation may be compared to a balanced scale, which has exactly the same weight on each side of the lever. If the weight is reduced on one side, the balance is disturbed. Thus to keep the balance, the weight must be reduced on the other side, too, by exactly the same amount. Any other changes in weights may be made, but they must be made so that the scale remains balanced.

How to transform an Equation

A scale is used to measure the weight of a object. On one side of the scale is placed an unknown weight and on the other side is placed a weight or weights of known value. The weights are adjusted until the scale is in balance. With the scale at the balanced position, the object of unknown weight weighs exactly the same as the object of known weight. Any change on one side only will disturb the balance.

Similarly, an equation is used to determine the unknown value of a term if all other terms in the equation are known. The unknown value is most commonly indicated by the letter x, but y and z are also often used. The other terms may be numerical or literal terms, but they are considered to be known. To repeat: In order to find an unknown term in an equation, all the other terms must be known.

Here you will study how the unknown value, or the unknown, may be found from the equation. It is necessary to change, or transform, the equation so that the unknown term, or letter, remains alone on one side of the equation.