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The given equation is:

\[
|3 + x| = -\frac{1}{2}
\]

However, the equation involves an absolute value on the left-hand side. The absolute value of any real number is always non-negative, meaning it is always either zero or positive. Therefore, the absolute value can **never be equal to a negative number** like \(-\frac{1}{2}\).

Thus, this equation has **no solution**.

Would you like more details or have any questions?

### Related Questions:
1. What are the properties of absolute value functions?
2. How do you solve absolute value equations when the right-hand side is positive?
3. What happens if the absolute value is set equal to zero?
4. Can complex numbers be involved in absolute value equations?
5. How do you graph absolute value functions?

### Tip:
Always remember, absolute value expressions cannot yield negative values. If an equation requires this, there is no real solution.

Learn why the equation |3 + x| = -1/2 has no solution. Absolute value expressions can never be equal to a negative number. This problem explains the properties of absolute value and how to approach such equations. Suitable for students in Grades 7-9.

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