If "3" is not a number (see Mathemagician Philosophy ; it is a symbol that represents a number) then there is no reason why "x" cannot represent a number.  When someone thinks of three, the unit (dogs, rocks, or days) is arbitrary.  Our number system uses "one", addition, subtraction, multiplication, division in any number of combinations.  The representation of a number as an arbitrary symbol like "x" reveals patterns within our Real and Complex number systems.  Elementary Algebra is the study of these patterns and it can be learned easier and made simplier through individualized tutoring. 

For example, remember that addition and subtraction are the same thing.  Subtracting is adding negative numbers.  This way you can add or subtract in any order as long as the sign goes with the term. 

Wikipedia link to Algebra