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

To solve the inequality \(-9(2x + 4) > -15x\), follow these steps:

### Step 1: Distribute the \(-9\) on the left side.
Distribute \(-9\) to both terms inside the parentheses:

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

So, the inequality becomes:
\[
-18x - 36 > -15x
\]

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

\[
-36 > 3x
\]

### Step 3: Solve for \(x\).
Divide both sides by \(3\) to solve for \(x\):

\[
-12 > x
\]

This can also be written as:
\[
x < -12
\]

### Solution:
The inequality that describes all the solutions is:
\[
x < -12
\]

Would you like more details or have any questions about this solution?

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Here are 5 questions to expand your understanding:

1. What would change in the solution if the inequality were \(-9(2x + 4) < -15x\)?
2. How does distributing the \(-9\) affect the inequality?
3. Why do we move all the \(x\) terms to one side of the inequality?
4. What would happen if you divided both sides by a negative number in this problem?
5. How can you verify that your solution \(x < -12\) is correct?

**Tip:** Always double-check the direction of your inequality after dividing or multiplying by a negative number.

Learn how to solve the inequality -9(2x + 4) > -15x step-by-step with detailed explanations. This problem covers inequalities, the distributive property, and solving equations. Suitable for students in Grades 7-9.

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