Q1. - Algebra 2

Question

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

Step-by-Step Solution

Answer

The absolute value of a number is always nonnegative.

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..