vWhich inequality describes all the solutions to −9(2*x* + 4) > −15*x*?

A.*x* <12111211

B.*x* >−1211−1211

C.*x* < −12

D.*x* > 3


To solve the inequality \(-9(2x + 4) > -15x\), let's work through the steps:

1. **Distribute the \(-9\) on the left side:**

   \[
   -9(2x + 4) = -18x - 36
   \]

   So, the inequality becomes:

   \[
   -18x - 36 > -15x
   \]

2. **Add \(18x\) to both sides to get all the \(x\) terms on one side:**

   \[
   -36 > 3x
   \]

3. **Divide both sides by 3 to solve for \(x\):**

   \[
   x < -12
   \]

Thus, the inequality that describes all the solutions is:

**C. \(x < -12\)**

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the solution change if the inequality were \(-9(2x + 4) < -15x\)?
2. Can you solve a similar inequality with different coefficients?
3. What happens to the inequality sign when dividing by a negative number?
4. How would you graph the solution \(x < -12\) on a number line?
5. What are some real-world applications of solving linear inequalities?

**Tip:** When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

Learn how to solve the inequality -9(2x + 4) > -15x with a detailed step-by-step solution. This problem covers key concepts in inequalities and linear equations, including the distributive property. Suitable for high school students in Grades 9-12.

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