Let's solve the equation:

\[
3 + |5x - 4| = -8
\]

### Step 1: Isolate the absolute value expression.
To isolate the absolute value, subtract 3 from both sides:

\[
|5x - 4| = -8 - 3
\]

\[
|5x - 4| = -11
\]

### Step 2: Analyze the absolute value condition.
Absolute values are always non-negative, meaning that \( |5x - 4| \geq 0 \) for any value of \( x \). 

However, here we have \( |5x - 4| = -11 \), which is impossible because an absolute value cannot be negative.

### Conclusion:
This equation has **no solution**.

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Would you like more details or have any further questions?

Here are some related questions:
1. What is the general method for solving absolute value equations?
2. How do you graph absolute value functions?
3. What happens when the absolute value term equals zero?
4. Can absolute values be used to represent distances?
5. How would the solution change if the right-hand side were positive?

**Tip:** Always check whether the equation makes sense before solving when dealing with absolute values.

Discover why the absolute value equation 3 + |5x - 4| = -8 has no solution, and learn key algebraic concepts like isolating the absolute value term. Understand why absolute values are always non-negative, making negative results impossible. Suitable for students in Grades 8-10.

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