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The equation given is:

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

Let's analyze this step by step:

1. **Absolute Value Properties**: The absolute value of any real number is always non-negative. This means that \( |x + 5| \geq 0 \) for all values of \( x \). Therefore, it is impossible for \( |x + 5| \) to equal a negative number like \(-3\).

2. **No Solution**: Since the absolute value of a number can never be negative, the equation has no solution. In other words, there is no value of \( x \) that satisfies \( |x + 5| = -3 \).

Thus, the correct answer is **A)** \( \emptyset \) (no solution).

Would you like more details, or do you have any further questions?

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Here are 5 follow-up questions for further learning:

1. What would be the solution if the equation was \( |x + 5| = 3 \)?
2. Can absolute value equations ever have negative solutions?
3. How can we graphically represent an absolute value function?
4. What happens if the absolute value function is less than a positive number, for example, \( |x + 5| < 4 \)?
5. How do you solve absolute value inequalities?

**Tip:** Always remember that absolute values are non-negative, so they can never equal a negative number.

Explore how to solve the absolute value equation |x + 5| = -3. Understand why no solutions exist and review key mathematical concepts such as the properties of absolute values. Suitable for middle school students (Grades 6-8).

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