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The equation you provided is:

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

However, absolute value expressions (denoted by the vertical bars \(|\cdot|\)) always result in a non-negative value. This means the absolute value of any real number is always greater than or equal to zero. Since the right-hand side of the equation is \(-3\), which is negative, there is no real solution to this equation.

In short:

\[
|3 + x| = -3 \quad \text{has no solution}.
\]

Would you like more details on this or any related concepts? Here are five related questions:

1. What is the general definition of absolute value?
2. How do you solve absolute value equations when the right side is positive?
3. What are the properties of absolute value functions?
4. Can absolute values be used with inequalities, and how?
5. How would this equation change if the right side were a positive number?

**Tip:** When solving absolute value equations, always check whether the equation is set equal to a negative number. If it is, there are no real solutions!

This page explains why the absolute value equation |3 + x| = -3 has no solution. Learn about the properties of absolute value and why it always results in a non-negative value. Suitable for students in Grades 7-9.

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