To solve the inequality [tex]\( z \leq -8 \)[/tex], we need to find all the numbers that are less than or equal to [tex]\(-8\)[/tex].
Let's analyze each number from the given list:
1. [tex]\(-16\)[/tex]: This number is less than [tex]\(-8\)[/tex], so it satisfies the inequality [tex]\( z \leq -8 \)[/tex].
2. [tex]\(-13\)[/tex]: This number is also less than [tex]\(-8\)[/tex], so it satisfies the inequality [tex]\( z \leq -8 \)[/tex].
3. [tex]\(-11\)[/tex]: This number is less than [tex]\(-8\)[/tex], so it satisfies the inequality [tex]\( z \leq -8 \)[/tex].
4. [tex]\(-9\)[/tex]: This number is less than [tex]\(-8\)[/tex], so it satisfies the inequality [tex]\( z \leq -8 \)[/tex].
5. [tex]\(-8.1\)[/tex]: This number is less than [tex]\(-8\)[/tex], so it satisfies the inequality [tex]\( z \leq -8 \)[/tex].
6. [tex]\(-8.01\)[/tex]: This number is less than [tex]\(-8\)[/tex], so it satisfies the inequality [tex]\( z \leq -8 \)[/tex].
7. [tex]\(-8.001\)[/tex]: This number is less than [tex]\(-8\)[/tex], so it satisfies the inequality [tex]\( z \leq -8 \)[/tex].
8. [tex]\(-8\)[/tex]: This number is equal to [tex]\(-8\)[/tex], so it satisfies the inequality [tex]\( z \leq -8 \)[/tex].
9. [tex]\(-7.999\)[/tex]: This number is greater than [tex]\(-8\)[/tex], so it does not satisfy the inequality [tex]\( z \leq -8 \)[/tex].
10. [tex]\(-7.99\)[/tex]: This number is greater than [tex]\(-8\)[/tex], so it does not satisfy the inequality [tex]\( z \leq -8 \)[/tex].
11. [tex]\(-7.9\)[/tex]: This number is greater than [tex]\(-8\)[/tex], so it does not satisfy the inequality [tex]\( z \leq -8 \)[/tex].
12. [tex]\(-7\)[/tex]: This number is greater than [tex]\(-8\)[/tex], so it does not satisfy the inequality [tex]\( z \leq -8 \)[/tex].
13. [tex]\(-5\)[/tex]: This number is greater than [tex]\(-8\)[/tex], so it does not satisfy the inequality [tex]\( z \leq -8 \)[/tex].
14. [tex]\(-3\)[/tex]: This number is greater than [tex]\(-8\)[/tex], so it does not satisfy the inequality [tex]\( z \leq -8 \)[/tex].
Therefore, 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]
