To determine the value of [tex]\( y \)[/tex] given that [tex]\( x \)[/tex] is 11, follow the steps below:
1. Firstly, we have the equation for [tex]\( y \)[/tex] as:
[tex]\[
y = |x| - 11
\][/tex]
2. We are given that [tex]\( x = 11 \)[/tex].
3. Next, substitute [tex]\( x \)[/tex] into the equation:
[tex]\[
y = |11| - 11
\][/tex]
4. The absolute value of 11 is 11, because the absolute value function [tex]\( |\cdot| \)[/tex] returns the non-negative value of a number:
[tex]\[
|11| = 11
\][/tex]
5. Now, perform the subtraction:
[tex]\[
y = 11 - 11
\][/tex]
6. Subtract 11 from 11 to find the value of [tex]\( y \)[/tex]:
[tex]\[
y = 0
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] is [tex]\(\boxed{0}\)[/tex].
