Sometimes, it is useful to restrict our attention over non-negative real numbers only. For this purpose, we define numerical or non-negative value of a real number which we call an absolute value or modulus of the real number.
            Absolute Value: The absolute value of a real number, denoted by, is the real number according as a positive, negative, or zero.
i.e.                   
            From the definition of absolute value of a real number, we have

Example:
            (1)   ,
            (2),
            (3)   .

Example:
            (1) ,
            (2) .

Example:
            (1) ,
            (2) .

Example:
            If , then .
Solution:
            We have
           
                     
                     
                     
                     

Example:
            For all real number,  and, .
Solution:
            Here, for all real numbers  and, we have