Absolute value is an operation in mathematics, written as bars on either side of the expression. For example, the absolute value of -1 is written as |-1|.

Absolute value can be thought of in three ways. First, the absolute value of any number is defined as the positive of that number. For example, |8| =8 and |-8| = 8. Second, one absolute value equation can yield two solutions.

For example, if we solve the equation |x| = 2, not only does x= 2 but also x =-2 because  |2|= 2 and |-2| = 2.

Third, absolute value is defined as the distance, without regard to direction, that any number is from 0 on the  real number line. Consider a formula for the distance on the real number line as  |k – 0|, in which k is any real number. Then, for example, the distance that 11 is from 0 would be 11 (because  |11 -0| =11). Likewise, the absolute value of 11 is equal to 11. The distance for -11 will also equal 11 (because  |-11 – 0| = |-11|= 11), and the absolute value of -11 is 11.

Thus, the absolute value of any real number is equal to the absolute value of its distance from 0 on the number line. Furthermore, if the absolute value is not used in the above formula  |k – 0|, the result for any negative number will be a negative distance. Absolute value helps improve formulas in order to obtain realistic solutions.  

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Reference

Barry Max Brandenberger, Jr.(2002). Mathematics. Macmillan Reference USA. pag (3)