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The inequality you have provided is:

\[
|5p + 2| < -4
\]

However, the absolute value of any real number is always non-negative, meaning \( |x| \geq 0 \) for any \( x \). Therefore, it is impossible for the absolute value of an expression to be less than a negative number. 

Hence, this inequality has **no solution**.

Would you like further details or explanations? Here are some related questions to explore:

1. What does the absolute value represent in mathematical terms?
2. Can an absolute value inequality ever have a negative value?
3. How would you solve an inequality involving absolute values and a positive number?
4. What happens if the inequality sign is reversed, like \( |5p + 2| > 4 \)?
5. Can you visualize absolute value inequalities on a number line?

**Tip:** When solving inequalities with absolute values, always check if the inequality is even possible, especially when comparing with negative numbers!

Explore why the absolute value inequality |5p + 2| < -4 has no solution. This problem highlights key concepts in algebra, including absolute values and inequalities, and demonstrates why absolute values cannot be less than a negative number.

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