Let's solve the inequality step by step to determine which option is correct.

We start with the inequality:

$-9(2x + 4) > -15x$

Step 1: Distribute the $-9$ on the left side.

$-18x - 36 > -15x$

Step 2: Add $18x$ to both sides to move the $x$ terms to one side.

$-36 > 3x$

Step 3: Divide both sides by 3 to solve for $x$.

$-12 > x$ This can be rewritten as: $x < -12$

Conclusion:

The correct inequality that describes all the solutions is $x < -12$.

Thus, the correct answer is D. $x < -12$.

Would you like more details or have any questions? Here are some related questions:

1. What happens if we reverse the inequality direction by multiplying or dividing by a negative number?
2. Can you graph the solution $x < -12$ on a number line?
3. How would the solution change if the inequality was $-9(2x + 4) \geq -15x$?
4. What is the impact of changing the constant term $-36$ in the inequality?
5. How would the solution set change if the original inequality were an equation instead?

Tip: Always be careful when dividing or multiplying inequalities by negative numbers; it reverses the inequality sign.