Question

Explain why the absolute value of a number is always nonnegative, $\left|a\right|$can equal $-a$.

Short answer

The absolute value of a number is always nonnegative.

Step-by-step solution

Step 1- Apply the concept of absolute value.

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Step 2- Step description.

Let $x\in \mathrm{ℝ}$be a real number, then its absolute value is denoted by $\left|x\right|$and defined as$\left|x\right|=\{\begin{array}{cc}x& x\ge 0\\ -x& x<0\end{array}$

Step 3- Step description.

The absolute value of a negative numbers is $|-x|=x$

For example: The absolute value of some negative numbers is as follows:

$\begin{array}{l}|-4|=4\\ |-10|=10\\ |-152|=152\end{array}$

Therefore, the absolute value of a number is always nonnegative..