Answer: C. $x<-5$

Explanation:1. Simplify the second inequality for y: Given $\dfrac{y}{6}>9$. Multiply both sides by $6$: $y > 9 \times 6$ $y > 54$.

2. Combine the inequalities: We have two inequalities for y: 1) $y < 24 - 6x$ 2) $y > 54$ Since y must be greater than $54$ and also less than $24-6x$, we can write: $54 < y < 24 - 6x$. For such a y to exist, the upper bound must be greater than the lower bound: $54 < 24 - 6x$.

3. Solve the resulting inequality for x: $54 < 24 - 6x$ Subtract $24$ from both sides: $54 - 24 < -6x$ $30 < -6x$ Divide by $-6$. Remember to reverse the inequality sign when dividing by a negative number: $\dfrac{30}{-6} > \dfrac{-6x}{-6}$ $-5 > x$ This can be rewritten as $x < -5$.

4. Check the solution with the options: The inequality representing the x values is $x < -5$. This matches option [C].

5. Conclusion: The inequality that represents the x values for all solutions $(x, y)$ that satisfy the given system of inequalities is $x<-5$.