Variable

Suppose you are going to buy a bicycle and you know it's price is 90$ and you also heard that there is a discount offer going on and you don't know what is the amount of discount. Then what will be the total price of that bicycle?

Total Price = 90$- Deduction 

So, if the discount is 10%(When you go to shop you see that 10% discount is going on) then the price is 

Total Price = 90$ - 10%

              = 90$ - 9$

       = 81$

So, the final price is 81$.

This unknown quantity of discount can be said as 'Variable' in mathematical context and a variable is just a symbol that can represent different values in an expression. So, in following expression Deduction is variable.

Total Price = 90$- Deduction 

It is representing different varying values, that's why called it variable.

In mathematics, variables are usually denoted by letters such as x,y,z,u,v etc.

So, the above expression can be written as 

Total Price = 90$ - X (Here X will be 10%)

Following are the example of variables:

x + 6

z + 10 

23y

x,z,y are example of variables. 

Continuous Variable:
If a variable x  can successively take all the values from a given number 'a' to another given number 'b', then x is called a continuous variable; otherwise, it is called a discrete variable.
The domain or interval of x in this case is denoted by a <= x <= b 

If a is omitted from the domain, it is indicated as a < x <= b  and it is said to be open at the left end.
The domain a <= x <= b is said to be closed and a < x < b is  open at both end.