To determine which algebraic expression has a term with a coefficient of 9, we need to examine each option carefully.
### Option A: [tex]\(6x - 9\)[/tex]
- The expression consists of two terms: [tex]\(6x\)[/tex] and [tex]\(-9\)[/tex].
- In the term [tex]\(6x\)[/tex], the coefficient is [tex]\(6\)[/tex].
- The term [tex]\(-9\)[/tex] is a constant, which does not have a variable.
- Hence, there is no term with a coefficient of 9.
### Option B: [tex]\(6(x + 5)\)[/tex]
- Distribute [tex]\(6\)[/tex] over the terms inside the parentheses.
- This gives us [tex]\(6 \cdot x + 6 \cdot 5\)[/tex], which simplifies to [tex]\(6x + 30\)[/tex].
- The term [tex]\(6x\)[/tex] has a coefficient of [tex]\(6\)[/tex].
- The term [tex]\(30\)[/tex] is a constant and does not involve the variable [tex]\(x\)[/tex].
- Hence, there is no term with a coefficient of 9.
### Option C: [tex]\(9x \div 6\)[/tex]
- This expression can be rewritten as [tex]\(\frac{9x}{6}\)[/tex].
- Simplified, this fraction becomes [tex]\(\frac{3}{2}x\)[/tex].
- Although this term can be expressed as [tex]\(\frac{3}{2}x\)[/tex], the original coefficient provided was 9.
### Option D: [tex]\(6 + x - 9\)[/tex]
- This expression consists of three terms: [tex]\(6\)[/tex], [tex]\(x\)[/tex], and [tex]\(-9\)[/tex].
- The term [tex]\(x\)[/tex] can be considered as [tex]\(1x\)[/tex], where the coefficient is [tex]\(1\)[/tex].
- The term [tex]\(6\)[/tex] and the term [tex]\(-9\)[/tex] are constants.
- Hence, there is no term with a coefficient of 9.
### Conclusion
Among all the given expressions, the only expression that originally has a term involving the coefficient of 9 is option C [tex]\(\frac{9x}{6}\)[/tex].
Therefore, the correct answer is option C.
