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The question is asking which absolute value inequalities will have all real solutions. To analyze this, let's break down each inequality:

### 1. \(|3x - 6| + 17 > 15\)
   \[
   |3x - 6| + 17 > 15
   \]
   Subtract 17 from both sides:
   \[
   |3x - 6| > -2
   \]
   Since the absolute value of any expression is always non-negative, it is always greater than or equal to 0. Therefore, this inequality is always true for all real values of \(x\). This inequality will have all real solutions.

### 2. \(|5x - 7| < -2\)
   \[
   |5x - 7| < -2
   \]
   Since the absolute value is always non-negative, it can never be less than a negative number. Thus, this inequality has no solutions.

### 3. \(|5x - 4| > -8\)
   \[
   |5x - 4| > -8
   \]
   Similar to the first inequality, the absolute value is always non-negative, and it will always be greater than any negative number. Therefore, this inequality will always be true for all real values of \(x\).

### 4. \(-2|3x - 5| \geq 3\)
   \[
   -2|3x - 5| \geq 3
   \]
   First, divide both sides by \(-2\), remembering to reverse the inequality:
   \[
   |3x - 5| \leq -\frac{3}{2}
   \]
   Again, since the absolute value is non-negative, it cannot be less than or equal to a negative number. Therefore, this inequality has no solutions.

### Final Answer:
- The inequalities that have all real solutions are:
   - \(|3x - 6| + 17 > 15\)
   - \(|5x - 4| > -8\)

Would you like further details or explanations on this? 

Here are five related questions to deepen your understanding:
1. How do you solve absolute value inequalities in general?
2. What happens when the absolute value inequality involves a negative comparison?
3. Can an absolute value inequality ever be less than a negative number?
4. How do you graph absolute value inequalities?
5. What are the common mistakes to avoid when solving absolute value inequalities?

**Tip:** When solving absolute value inequalities, always remember that the absolute value is never negative, and this fact is crucial when determining if the inequality has solutions.

Which absolute value inequalities will have all real solutions as a solution set?

Understand which absolute value inequalities will have all real solutions. Learn about properties of absolute values, key inequalities, and find the solutions with step-by-step explanations. Suitable for high school students in Grades 9-12.

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