Let's analyze each statement about the inequality [tex]\(6x > 99\)[/tex].
To solve this, we need to check whether each given value of [tex]\(x\)[/tex] satisfies the inequality.
### Statement a: 0 is a solution.
- Substitute [tex]\(x = 0\)[/tex] into the inequality.
- [tex]\(6 \cdot 0 = 0\)[/tex]
- Check if [tex]\(0 > 99\)[/tex].
[tex]\(0\)[/tex] is not greater than [tex]\(99\)[/tex], so this statement is False.
### Statement b: 13 is a solution.
- Substitute [tex]\(x = 13\)[/tex] into the inequality.
- [tex]\(6 \cdot 13 = 78\)[/tex]
- Check if [tex]\(78 > 99\)[/tex].
[tex]\(78\)[/tex] is not greater than [tex]\(99\)[/tex], so this statement is False.
### Statement c: 16.5 is a solution.
- Substitute [tex]\(x = 16.5\)[/tex] into the inequality.
- [tex]\(6 \cdot 16.5 = 99\)[/tex]
- Check if [tex]\(99 > 99\)[/tex].
[tex]\(99\)[/tex] is not greater than [tex]\(99\)[/tex]; it is equal. Therefore, this statement is False.
### Statement d: 64 is a solution.
- Substitute [tex]\(x = 64\)[/tex] into the inequality.
- [tex]\(6 \cdot 64 = 384\)[/tex]
- Check if [tex]\(384 > 99\)[/tex].
[tex]\(384\)[/tex] is indeed greater than [tex]\(99\)[/tex], so this statement is True.
### Statement e: There is only one solution.
From the previous checks:
- [tex]\(x = 0\)[/tex] does not satisfy the inequality.
- [tex]\(x = 13\)[/tex] does not satisfy the inequality.
- [tex]\(x = 16.5\)[/tex] does not satisfy the inequality.
- [tex]\(x = 64\)[/tex] satisfies the inequality.
Since only [tex]\(x = 64\)[/tex] satisfies the inequality from the given options, the statement that there is only one solution in the given set of values is True.
### Summary:
- a. [tex]\(0\)[/tex] is a solution. False
- b. [tex]\(13\)[/tex] is a solution. False
- c. [tex]\(16.5\)[/tex] is a solution. False
- d. [tex]\(64\)[/tex] is a solution. True
- e. There is only one solution. True
