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

A.*x* >−1211−1211

B.*x* > 3

C.*x* <12111211

D.*x* < −12


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.

Learn how to solve the inequality -9(2x + 4) > -15x step-by-step. Understand the application of inequalities, the distributive property, and solving linear equations. Suitable for high school students.

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