https://file.aiquickdraw.com/mathbot/file/1726114529613ljji1368.jpg

The equation given in the image is:

\[
-6 + 6|3x + 4| = 12
\]

Let's solve it step-by-step:

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

\[
6|3x + 4| = 12 + 6
\]

\[
6|3x + 4| = 18
\]

2. **Divide both sides by 6:**

\[
|3x + 4| = 3
\]

3. **Consider both cases for the absolute value:**

- Case 1: \(3x + 4 = 3\)
- Case 2: \(3x + 4 = -3\)

**Solve each case:**

- **Case 1:**

\[
3x + 4 = 3 \implies 3x = -1 \implies x = -\frac{1}{3}
\]

- **Case 2:**

\[
3x + 4 = -3 \implies 3x = -7 \implies x = -\frac{7}{3}
\]

4. **Solutions:**

\[
x = -\frac{1}{3} \quad \text{and} \quad x = -\frac{7}{3}
\]

So, the solutions to the equation are:

\[
x = -\frac{1}{3}, \; x = -\frac{7}{3}
\]

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

### Related Questions:
1. How do you solve equations with multiple absolute value expressions?
2. What are the properties of absolute value that help solve equations?
3. How do absolute values impact inequalities?
4. Can absolute value equations have no solution?
5. How do you graph an absolute value function?

**Tip:** Always check both possible cases when solving equations involving absolute values.

Learn how to solve the absolute value equation -6 + 6|3x + 4| = 12 with a detailed step-by-step solution. This problem covers key algebraic concepts such as isolating the absolute value and solving two cases. Suitable for students in Grades 9-11.

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