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To determine which absolute value inequalities have no solution, let's analyze each inequality one by one.

1. **\( |5x - 4| \geq -8 \)**  
   The absolute value of any expression is always non-negative (i.e., \( |A| \geq 0 \) for any real \( A \)). Therefore, any absolute value expression will always be greater than or equal to a negative number.  
   This inequality is always true because \( |5x - 4| \) is non-negative, and it is always greater than or equal to \(-8\).  
   **This inequality has a solution.**

2. **\( |3x - 6| + 17 > 15 \)**  
   First, simplify the inequality:  
   \[
   |3x - 6| + 17 > 15 \quad \Rightarrow \quad |3x - 6| > -2
   \]  
   Again, since the absolute value of any expression is always non-negative, \( |3x - 6| \geq 0 \). Since \( |3x - 6| \) is always greater than or equal to 0, it will definitely be greater than \(-2\).  
   **This inequality always has a solution.**

3. **\( |5x - 7| < -2 \)**  
   The absolute value of any expression cannot be negative. Therefore, the inequality \( |5x - 7| < -2 \) has **no solution** because an absolute value can never be less than a negative number.  
   **This inequality has no solution.**

4. **\( -2|3x - 5| \geq 3 \)**  
   First, divide both sides by \(-2\), which reverses the inequality:  
   \[
   |3x - 5| \leq -\frac{3}{2}
   \]  
   Since the absolute value is always non-negative, \( |3x - 5| \geq 0 \), and it is impossible for it to be less than or equal to a negative number.  
   **This inequality has no solution.**

### Summary
The inequalities that have **no solution** are:
- \( |5x - 7| < -2 \)
- \( -2|3x - 5| \geq 3 \)

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you solve absolute value equations and inequalities?
2. What happens when you divide or multiply both sides of an inequality by a negative number?
3. Can an absolute value expression ever be negative?
4. How do you interpret inequalities that involve absolute values?
5. What is the difference between solving an inequality and an equation?

**Tip**: When solving inequalities, always be cautious when dividing or multiplying by negative numbers, as it reverses the inequality sign!

Which absolute value inequalities have no solution? (Select all that apply.)

Learn how to determine which absolute value inequalities have no solution. This guide covers properties of absolute value and how to handle inequalities involving absolute value expressions, suitable for students in Grades 9-11.

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