What is algebra ?

I guess the first thing  that that come in your mind are those x, y and Z which give you so much anxiety. in fact, you might ask why not stick to simple operation like addition (+), subtraction (-),multiplication and division (:).

but what happen when you want to make generalization. Lets say you want to represent all  the following numbers :      (5, 10, 15, 20,  25, 30...........)

what if I told you there is simple way to represent all those number with a simple expression.In fact if you look deep in these numbers you will find a structure where there is a a common factor or a pattern.
here are the list of these numbers one more time (5, 10, 15, 20,  25, 30...........), can you try to find a structure, a pattern between the elements of this set ? eureka !!! they are all multiple of 5 which give you this new form (  5x1, 5x2, 5x3, 5x4, 5x5, 5x6,.........)

The algebraic way to write this set of number is simple we just have write 5x where x represent the set of Natural whole number .   5x stand for 5 time x there is an agreement to get rid of the multiplication sign when using letter and number 

as we can see by trying to understand the structure  of a this set we can use simple expression to represent all of them. Letter come handy when it come to generalization.

the purpose of algebra is the use of symbol like  x, y, z to make generalization.

algebra can be also be  inductive  by trying to find the necessary  condition  get a specific result .  You usually compute your operation  easily and get your result like  5 + 2  =  7. Lets  say your want a specific result you are looking for the necessary input to reach this specific result, in this case you are trying to move backward by deconstructing an operation to find out one of its element.

Let say you want to get 12 by adding 8 to an another number. you question can be written like that  :      ?  +  8  = 12 you can easily guess the ? has to be 4 to get 12 .  instead of a question mark algebra would use a  symbol like x   :    x + 8 = 12

to move backward you have to do a deconstruction of the operation of addition which a subtraction so    x =12-8

to sum up algebra use inductive and deductive approach to structure , made generalization, algebra is an language that go underneath of the reality in order to reveal the structure of this reality and make is understandable.

Click the links below to watch some examples of free math video

converting logarithmic expression in to exponential form

solution of equation with addition using two logarithms