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.