Page 50 - MarceAlgebra Demystified

CHAPTER 2

Introduction to

Variables

A variable is a symbol for a number whose value is unknown. A variable
might represent quantities at different times. For example if you are paid by
the hour for your job and you earn $10 per hour, letting x represent the
number of hours worked would allow you to write your earnings as ‘‘10x.’’
The value of your earnings varies depending on the number of hours worked.
If an equation has one variable, we can use algebra to determine what value
the variable is representing.
Variables are treated like numbers because they are numbers. For instance
2 þ x means two plus the quantity x and 2x means two times the quantity x
(when no operation sign is given, the operation is assumed to be
multiplication). The expression 3x þ 4 means three times x plus four.
This is not the same as 3x þ 4x which is three x’s plus four x’s for a total
of seven x’s: 3x þ 4x ¼ 7x.
If you are working with variables and want to check whether the expression
you have computed is really equal to the expression with which you started,
take some larger prime number, not a factor of anything else in the expression,
and plug it into both the original expression and the last one. If the resulting
numbers are the same, it is very likely that the first and last expressions are
equal. For example you might ask ‘‘Is it true that 3x þ 4 ¼ 7x?’’ Test x ¼ 23:

37

Copyright 2003 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.