The equation \( |x - 6| = -1 \) has no solution.

This is because the absolute value of any expression is always non-negative (i.e., \( |x - 6| \geq 0 \) for all \(x\)). Therefore, it cannot equal a negative number, such as \(-1\) in this case.

### Conclusion:
- Since an absolute value cannot be negative, there is no real solution to this equation.

Would you like a detailed explanation or have any further questions?

Here are 5 related questions:
1. What are the properties of absolute value functions?
2. How would the equation change if it was \( |x - 6| = 1 \)?
3. Can absolute value equations have no solution in some cases?
4. How do we solve \( |x - 6| = c \) if \(c\) is a positive number?
5. What happens if we square both sides of an absolute value equation?

**Tip:** Absolute value represents the distance from zero on a number line, and distance is always non-negative.

Explore why the absolute value equation |x - 6| = -1 has no solution. Understand the core concepts of absolute value and why it cannot equal a negative number. This explanation is ideal for students in Grades 7-9.

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