Which inequality describes all the solutions to −9(2x + 4) > −15x?
A.x < −12
B.x <1211

C.x > 3
D.x >−1211


Let's solve the inequality \(-9(2x + 4) > -15x\):

1. **Distribute the \(-9\)** on the left-hand side:
   \[
   -9(2x) - 9(4) > -15x
   \]
   This simplifies to:
   \[
   -18x - 36 > -15x
   \]

2. **Move the terms involving \(x\) to one side**:
   Add \(18x\) to both sides:
   \[
   -36 > -15x + 18x
   \]
   Simplifying:
   \[
   -36 > 3x
   \]

3. **Solve for \(x\)**:
   Divide both sides by 3:
   \[
   \frac{-36}{3} > x
   \]
   Simplifying:
   \[
   -12 > x
   \]
   Or equivalently:
   \[
   x < -12
   \]

The correct answer is:
**A. \(x < -12\)**

Would you like more details on any step or have any questions?

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Here are 5 related questions to explore:

1. How do you solve inequalities with negative coefficients?
2. What happens when you divide or multiply both sides of an inequality by a negative number?
3. Can an inequality have more than one solution?
4. What is the difference between "greater than" and "greater than or equal to" in inequalities?
5. How can inequalities be represented graphically on a number line?

**Tip**: Always remember that when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign!

Which inequality describes all the solutions to −9(2x + 4) > −15x?
A. x < −12
B. x < 12
C. x > 3
D. x > −12

Discover how to solve the linear inequality −9(2x + 4) > −15x. This problem covers algebraic concepts such as the distributive property and rules for solving inequalities. Follow the detailed step-by-step solution suitable for students in Grades 7-9.

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