4) define absolute value

Brief Explanations:

The absolute value of a real - number (x), denoted as (|x|), is the non - negative value of (x) without regard to its sign. Mathematically, if (x\geq0), then (|x| = x); if (x<0), then (|x|=-x). It represents the distance of the number from zero on the number line.

Answer:

The absolute value of a real number (x), denoted as (|x|), is defined as (|x|=\begin{cases}x, & x\geq0\ -x, & x < 0\end{cases}), and it represents the distance of (x) from 0 on the number line.