Sure, let's solve the problem step-by-step.
We are given the equation for [tex]\( y \)[/tex] as:
[tex]\[ y = |x| - 7 \][/tex]
1. First, we need to know the value of [tex]\( x \)[/tex]. According to the problem, [tex]\( x \)[/tex] is [tex]\(-1\)[/tex].
2. Next, we substitute [tex]\( x = -1 \)[/tex] into the equation. The equation becomes:
[tex]\[ y = |-1| - 7 \][/tex]
3. The absolute value function [tex]\( |x| \)[/tex] outputs the non-negative value of [tex]\( x \)[/tex]. Therefore, [tex]\(|-1|\)[/tex] equals 1 because the absolute value of [tex]\(-1\)[/tex] is 1.
4. Now substitute back into the equation:
[tex]\[ y = 1 - 7 \][/tex]
5. Perform the subtraction:
[tex]\[ y = 1 - 7 = -6 \][/tex]
So, the value of [tex]\( y \)[/tex] is [tex]\(-6\)[/tex].
