Answer:
Option c
[tex]y\geq-3[/tex] or [tex]y \leq 21[/tex]
Step-by-step explanation:
The absolute value is a function that transforms any value x into a positive number.
Therefore, for the function [tex]f(x) = |x|[/tex] x> 0 for all real numbers.
Then the inequation:
[tex]|y-9| \leq 12[/tex] has two cases
[tex](y-9)[/tex] if [tex]y \geq 9[/tex] (i)
[tex]-(y-9)[/tex] if [tex]y < 9[/tex] (ii)
We solve the case (i)
[tex]y \leq 9 + 12\\y\leq21[/tex]
We solve the case (ii)
[tex]-y +9 \leq 12\\-y \leq 12-9\\y \geq -3[/tex]
Then the solution is:
[tex]y\geq-3[/tex] or [tex]y \leq 21[/tex]
