Page:Elementary algebra (1896).djvu/73

55 Rh CHAPTER VII.

Simple Equations.

72. An equation asserts that two expressions are equal, but we do not usually employ the word equation in so wide a sense.

Thus the statement x+3+x = 2x+3, which is always true whatever value x may have, is called an identical equation, or an identity. The sign of identity frequently used is.

The parts of an equation to the right and left of the sign of equality are called members or sides of the equation, and are distinguished as the right side and left side.

73. Certain equations are only true for particular values of the symbols employed. Thus 3x= 6 is only true when x = 2, and is called an equation of condition, or more usually an equation. Consequently an identity is an equation which is always true whatever be the values of the symbols involved; whereas an equation, in the ordinary use of the word, is only true for particular values of the symbols. In the above example 3x = 6, the value 2 is said to satisfy the equation. The object of the present chapter is to explain how to treat an equation of the simplest kind in order to discover the value which satisfies it. 74. The letter whose value it is required to find is called the unknown quantity. The process of finding its value is called solving the equation. The value so found is called the root or the solution of the equation.

75. The solution of equations, and the operations subsidiary to it, form an extremely important part of Mathe-