To determine the value of [tex]\( y \)[/tex] given that [tex]\( x \)[/tex] is [tex]\(-11\)[/tex] and the relationship [tex]\( y = |x| + 4 \)[/tex], we will follow these steps:
1. Calculate the absolute value of [tex]\( x \)[/tex]:
- The absolute value of a number is its distance from zero on the number line without considering the direction. Mathematically, it is denoted by [tex]\( |x| \)[/tex].
- For [tex]\( x = -11 \)[/tex]:
[tex]\[
|x| = |-11| = 11
\][/tex]
2. Substitute the absolute value of [tex]\( x \)[/tex] into the formula for [tex]\( y \)[/tex]:
- The given formula is [tex]\( y = |x| + 4 \)[/tex].
- Now that we have [tex]\( |x| = 11 \)[/tex], we substitute it into the formula:
[tex]\[
y = 11 + 4
\][/tex]
3. Perform the addition to find [tex]\( y \)[/tex]:
- Adding 11 and 4 yields:
[tex]\[
y = 15
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is [tex]\(-11\)[/tex] is [tex]\( 15 \)[/tex].
