Question

solve for x.
|x| = 0
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.

Explanation:

Step1: Recall the definition of absolute value

The absolute value of a number \( x \), denoted as \( |x| \), is the distance of \( x \) from 0 on the number line. By definition, \( |x|=

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

\)

Step2: Solve \( |x| = 0 \)

We want to find all real numbers \( x \) such that the distance from \( x \) to 0 is 0. The only number whose distance from 0 is 0 is 0 itself. So, if \( |x|=0 \), then \( x = 0 \) (because when \( x = 0 \), both cases of the absolute - value definition give \( |0|=0 \); if \( x>0 \), \( |x|=x>0
eq0 \), and if \( x < 0 \), \( |x|=-x>0
eq0 \))

Answer:

\( 0 \)