To find the values of [tex]\( z \)[/tex] that satisfy the inequality [tex]\( z \leq -8 \)[/tex], we need to examine each value from the provided list and determine whether it meets this condition. Let's go through the values one by one to see which ones satisfy the inequality.
Here is the list of values:
[tex]\[
-16, -13, -11, -9, -8.1, -8.01, -8.001, -8, -7.999, -7.99, -7.9, -7, -5, -3
\][/tex]
### Steps:
1. [tex]\( z = -16 \)[/tex]:
- Since [tex]\(-16 \leq -8\)[/tex] is true, [tex]\( -16 \)[/tex] is included.
2. [tex]\( z = -13 \)[/tex]:
- Since [tex]\(-13 \leq -8\)[/tex] is true, [tex]\( -13 \)[/tex] is included.
3. [tex]\( z = -11 \)[/tex]:
- Since [tex]\(-11 \leq -8\)[/tex] is true, [tex]\( -11 \)[/tex] is included.
4. [tex]\( z = -9 \)[/tex]:
- Since [tex]\(-9 \leq -8\)[/tex] is true, [tex]\( -9 \)[/tex] is included.
5. [tex]\( z = -8.1 \)[/tex]:
- Since [tex]\(-8.1 \leq -8\)[/tex] is true, [tex]\( -8.1 \)[/tex] is included.
6. [tex]\( z = -8.01 \)[/tex]:
- Since [tex]\(-8.01 \leq -8\)[/tex] is true, [tex]\( -8.01 \)[/tex] is included.
7. [tex]\( z = -8.001 \)[/tex]:
- Since [tex]\(-8.001 \leq -8\)[/tex] is true, [tex]\( -8.001 \)[/tex] is included.
8. [tex]\( z = -8 \)[/tex]:
- Since [tex]\(-8 \leq -8\)[/tex] is true, [tex]\( -8 \)[/tex] is included.
9. [tex]\( z = -7.999 \)[/tex]:
- Since [tex]\(-7.999 \leq -8\)[/tex] is false, [tex]\( -7.999 \)[/tex] is not included.
10. [tex]\( z = -7.99 \)[/tex]:
- Since [tex]\(-7.99 \leq -8\)[/tex] is false, [tex]\( -7.99 \)[/tex] is not included.
11. [tex]\( z = -7.9 \)[/tex]:
- Since [tex]\(-7.9 \leq -8\)[/tex] is false, [tex]\( -7.9 \)[/tex] is not included.
12. [tex]\( z = -7 \)[/tex]:
- Since [tex]\(-7 \leq -8\)[/tex] is false, [tex]\( -7 \)[/tex] is not included.
13. [tex]\( z = -5 \)[/tex]:
- Since [tex]\(-5 \leq -8\)[/tex] is false, [tex]\( -5 \)[/tex] is not included.
14. [tex]\( z = -3 \)[/tex]:
- Since [tex]\(-3 \leq -8\)[/tex] is false, [tex]\( -3 \)[/tex] is not included.
### Result:
The values that satisfy the inequality [tex]\( z \leq -8 \)[/tex] are:
[tex]\[
-16, -13, -11, -9, -8.1, -8.01, -8.001, -8
\][/tex]
