Question

find all numbers whose absolute value is 6. if there is more than one, separate them with commas. if there are no such numbers, click on
one\.

Explanation:

Step1: Recall absolute - value definition

The absolute - value of a number \(x\), denoted as \(|x|\), is defined as \(|x|=

$$\begin{cases}x, & x\geq0\\ - x, & x < 0\end{cases}$$

\). We want to find \(x\) such that \(|x| = 6\).

Step2: Solve for positive and negative cases

Case 1: If \(x\geq0\), then \(|x|=x\). So, \(x = 6\) satisfies \(|x| = 6\).
Case 2: If \(x<0\), then \(|x|=-x\). Setting \(-x = 6\), we get \(x=-6\).

Answer:

6, - 6