Basic Algebra can be described as "generalized arithmetics" [1
This is single most crucial concept in all algebra. A letter can be a number. In other words, a letter can be any number or a "variable".
Variables can be seen as 
So 3+3=2x3 is for instance an algebraic statement which can be generalized as x+x=2x where x is the "variable". The "x" can be any number you like.
The expression above is called an equation because it "compares" two different statement which MUST be equal both logically and mathematically (counting), The equation means that
But again, to be able to understand variables, you must work with them. I will take the example of Zoltan P.Dienes approach which I read in his 1960 book: "Buidling up mathematics" 
Algebra can bee seen as arithmetics where letters take the place of numbers.
Those letters are called "variables"
Variables can be seen as
From Basic Algebra back to the homepage
Source:1. Two Year College Mathematics Readings
2. Elementary and Middle School Mathematics: Teaching Developmentally (7th Edition)
. Zolan P. Dienes: "Building up Mathematics", Hutchinson Educational Ltd,
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Stay in touch with nature. It's full of mathematics!
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