To solve the equation [tex]\( |x| = 6 \)[/tex], we need to understand the concept of absolute value.
The absolute value of a number is its distance from 0 on the number line, regardless of direction. Therefore, for the equation [tex]\( |x| = 6 \)[/tex], we are looking for the numbers [tex]\( x \)[/tex] whose distance from 0 is 6.
We can break this down into two cases:
1. When [tex]\( x \)[/tex] is positive:
[tex]\[
|x| = x = 6
\][/tex]
So one solution is:
[tex]\[
x = 6
\][/tex]
2. When [tex]\( x \)[/tex] is negative:
[tex]\[
|x| = -x = 6
\][/tex]
Therefore:
[tex]\[
-x = 6 \implies x = -6
\][/tex]
Thus, the two possible values of [tex]\( x \)[/tex] that satisfy [tex]\( |x| = 6 \)[/tex] are:
[tex]\[
x = 6 \quad \text{and} \quad x = -6
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-6 \text{ or } 6}
\][/tex]
