Solve the following absolute value equation.
StartAbsoluteValue x minus 5 EndAbsoluteValueequalsminus1

The equation given is:

\[
|x - 5| = -1
\]

The absolute value of any expression is always non-negative, meaning it can never be less than 0. However, in this case, the equation is stating that the absolute value of something equals \(-1\), which is impossible.

Thus, **there is no solution** to this equation.

Would you like any further details or have any questions? Here are some related questions to consider:

1. What is the general approach to solving absolute value equations?
2. How do you solve absolute value inequalities?
3. What happens if the right-hand side of the equation was a positive number?
4. Can absolute value equations have more than one solution?
5. How would the graph of this absolute value function look?

**Tip:** Always check the validity of an absolute value equation before solving, especially when the right-hand side is a negative number.

Solve the following absolute value equation: |x - 5| = -1

Understand why the absolute value equation |x - 5| = -1 has no solution. This problem highlights key algebraic concepts about absolute values and the properties of absolute value functions. Suitable for middle school students in Grades 6-8.

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