Algebraic Equations:
There are two types of equations: identities & conditional equations. An identity is an equation which is true for all values of the unknown included. The identity sign (≡) is used in place of the equal sign to denote an identity. Therefore, x2 ≡ (x)(x), 3y + 5y ≡8y, and yx + yz ≡y(x + z) are all identities since they are true for all values of x, y, or z. A conditional equation is one which is true only for some particular value(s) of the literal number(s) involved. A conditional equation is 3x + 5 = 8, because only the value x = 1 satisfies the equation. While the word equation is used by itself, it commonly means a conditional equation.
The root(s) of an equation (conditional equation) is any value(s) of the literal number(s) in the equation which makes the equation true. Therefore, 1 is the root of the equation 3x + 5 = 8 since x = 1 makes the equation true. To solve an algebraic equation means to search the root(s) of the equation.
The application of algebra is practical because several physical problems can be solved using algebraic equations. For instance, pressure is described as the force which is applied divided through the area over which it is applied. Using the literal numbers P (to represent the pressure), F (to represent the force), and A (to represent the area over that the force is applied), this physical relationship can be written as the algebraic equation P (F/A). While the numerical values of the force, F, and the area, A, are called at a particular time, the pressure, P, can be computed by solving this algebraic equation. While this is a straightforward application of an algebraic equation to the solution of a physical problem, it describes the general approach which is used. Almost all physical problems are solved using this approach.