To determine which numbers are solutions to the equation [tex]\( |x| = 16 \)[/tex], we need to identify the values of [tex]\( x \)[/tex] that satisfy this equation. The absolute value [tex]\(|x|\)[/tex] of a number [tex]\( x \)[/tex] represents its distance from zero on the number line, irrespective of the direction (positive or negative). Thus, [tex]\(|x| = 16\)[/tex] implies that [tex]\( x \)[/tex] can be either 16 or -16.
Let's check each option to see if it satisfies [tex]\(|x| = 16\)[/tex]:
A. [tex]\( x = 16 \)[/tex]
When [tex]\( x = 16 \)[/tex]:
[tex]\[
|16| = 16
\][/tex]
This satisfies the equation. So, 16 is a solution.
B. [tex]\( x = -16 \)[/tex]
When [tex]\( x = -16 \)[/tex]:
[tex]\[
|-16| = 16
\][/tex]
This also satisfies the equation. So, -16 is a solution.
C. [tex]\( x = -4 \)[/tex]
When [tex]\( x = -4 \)[/tex]:
[tex]\[
|-4| = 4
\][/tex]
This does not satisfy the equation because [tex]\( 4 \neq 16 \)[/tex]. So, -4 is not a solution.
D. [tex]\( x = 4 \)[/tex]
When [tex]\( x = 4 \)[/tex]:
[tex]\[
|4| = 4
\][/tex]
This does not satisfy the equation because [tex]\( 4 \neq 16 \)[/tex]. So, 4 is not a solution.
E. [tex]\( x = 2 \)[/tex]
When [tex]\( x = 2 \)[/tex]:
[tex]\[
|2| = 2
\][/tex]
This does not satisfy the equation because [tex]\( 2 \neq 16 \)[/tex]. So, 2 is not a solution.
From the above analysis, the solutions to the equation [tex]\( |x| = 16 \)[/tex] are:
- 16 (Option A)
- -16 (Option B)
Therefore, the numbers that are solutions to the equation [tex]\(|x| = 16\)[/tex] are:
[tex]\[ \boxed{\text{A and B}} \][/tex]
