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The problem asks to determine the solution set for the inequality:

\[
|4x + 9| < 3
\]

### Steps to solve the inequality:

1. **Break down the absolute value inequality**:
   \[
   |4x + 9| < 3 \implies -3 < 4x + 9 < 3
   \]
   
2. **Isolate \(4x\)**:
   Subtract 9 from all sides:
   \[
   -3 - 9 < 4x < 3 - 9
   \]
   \[
   -12 < 4x < -6
   \]

3. **Solve for \(x\)**:
   Divide all terms by 4:
   \[
   -3 < x < -\frac{3}{2}
   \]

Thus, the solution to the inequality is:
\[
-3 < x < -\frac{3}{2}
\]

### Answer:
From the options, the correct one is:
- **Option a: \(-3 < x < -\frac{3}{2}\)**.

Would you like more details on this process or further clarification?

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Here are 5 related questions you can explore:

1. How do you solve absolute value inequalities involving a "greater than" condition?
2. What happens if the absolute value inequality has no solution?
3. How do you graph the solution of absolute value inequalities on a number line?
4. How would the solution change if the inequality were \( |4x + 9| \leq 3 \)?
5. What if the expression inside the absolute value were more complex, like \( |2x^2 + 3x + 1| < 5 \)?

**Tip**: Always remember to break down absolute value inequalities into two inequalities and solve both!

Tentukan himpunan penyelesaian dari pertidaksamaan berikut: |4x + 9| < 3

Learn how to solve the absolute value inequality |4x + 9| < 3 with a detailed solution. This problem covers key algebraic concepts and step-by-step methods to isolate the variable x. Suitable for students in Grades 10-12.

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