https://file.aiquickdraw.com/mathbot/file/17273210581534ertl58v.jpg

The equation you need to solve is:

\[
6 = 8 + |9x - 4|
\]

### Step-by-step solution:

1. **Isolate the absolute value:**

\[
6 - 8 = |9x - 4|
\]
\[
-2 = |9x - 4|
\]

2. **Analyze the result:**
   
An absolute value \( |A| \) is always non-negative, meaning it cannot be a negative number. Here, we have \( |9x - 4| = -2 \), which is impossible.

### Conclusion:
There is no solution to this equation because an absolute value cannot be negative.

Thus, the solution set is the **empty set**: \( \emptyset \).

Let me know if you need more details, and feel free to ask any of the following questions for further practice:

1. How do you solve equations involving absolute values?
2. Can you explain cases when an absolute value equation has no solution?
3. What is the general method for solving \( |Ax + B| = C \)?
4. How do you graph absolute value equations?
5. Can absolute values ever be negative?

**Tip**: Always check if the absolute value equation results in a negative value. If it does, there's no solution!

Learn how to solve the absolute value equation 6 = 8 + |9x - 4|. This step-by-step guide shows the solution and explains the key concepts involved, such as isolating the absolute value term and analyzing if the result is valid. Suitable for Grades 7-9.

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