In the most basic sense, algebra is the study of a set and one or more operations. The set comprises the objects we work with and operations are rules that produce an object based on the objects being operated upon (sounds a little convoluted at first).
At the very beginning of our mathematical experience, our objects are natural numbers and the operation is addition. Early on, we define other operations based on addition — subtraction, multiplication, division, exponentiation — which lead to questions that have answers not present in the set of natural numbers, so we enrich our set by adopting new elements. The number zero, negatives, rationals, irrationals, and complex numbers all come out of the need to answer some of these questions.
In order to be successful in studying the algebra of real numbers, it is important that we understand the basics of numbers and operations. Although you have developed many rules and algorithms for working with numbers, almost everything you do with numbers can be reduced to the following facts:
There are other issues — like our use of the base 10 system and specific mathematical notation — that we need to be aware of in our study, but do not affect the basics of algebra.
The backbone of our study is the ability to analyze the effects of operations on a multitude of numbers simultaneously. To do this we need a placeholder for a number that can have different values. This placeholder is called a variable. It is important to remember that variables are just numbers that we do not currently have a value for. They are not treated differently than known values — also called constants — except in the fact that the result of an operation involving a variable produces an unknown value.