To solve the equation \(-5|3 + 3x| + 6 = -9\), let's break it down step by step:

1. **Isolate the absolute value term:**

   \[
   -5|3 + 3x| + 6 = -9
   \]

   Subtract 6 from both sides:

   \[
   -5|3 + 3x| = -15
   \]

2. **Divide by \(-5\):**

   \[
   |3 + 3x| = 3
   \]

3. **Consider the two possible cases for the absolute value:**

   Case 1: \(3 + 3x = 3\)

   Case 2: \(3 + 3x = -3\)

4. **Solve for \(x\) in both cases:**

   - For \(3 + 3x = 3\):

     \[
     3x = 0 \implies x = 0
     \]

   - For \(3 + 3x = -3\):

     \[
     3x = -6 \implies x = -2
     \]

So the solutions to the equation are \(x = 0\) and \(x = -2\).

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

Here are some related questions:

1. What is the absolute value function, and how is it defined?
2. How do you solve an equation with an absolute value inequality?
3. Can absolute value equations have no solution? Explain with an example.
4. How do you handle absolute value equations with variables on both sides?
5. What are the general steps for solving absolute value equations?
6. How can we graph the absolute value function?
7. What happens if you multiply or divide both sides of an absolute value equation by a negative number?
8. How would the solution change if the absolute value expression had a different coefficient?

**Tip:** When solving absolute value equations, always consider the two possible cases resulting from the definition of absolute value.

Learn how to solve the absolute value equation -5|3 + 3x| + 6 = -9 step-by-step. This problem involves solving for x with absolute value and linear equations. Suitable for high school students.

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