https://file.aiquickdraw.com/mathbot/file/1727217108739crvdpi8x.jpg

The equation given in the image is:

\[
|x - 1| = -6
\]

Now let's analyze this step-by-step:

### Key Insight
An absolute value expression, such as \(|x - 1|\), is always **non-negative**, meaning it must be either zero or positive. However, the right-hand side of this equation is \(-6\), which is negative.

### Conclusion
Since an absolute value can **never be negative**, this equation has **no real solution**.

Thus, the correct answer is:
\[
\boxed{\text{NO REAL SOLUTION}}
\]

Would you like further explanation or more details? Here are some related questions for additional practice:

1. How would you solve \(|x - 2| = 5\)?
2. Can an absolute value equation ever have a negative solution? Why or why not?
3. What are the properties of absolute value functions?
4. How do you solve \(|x + 3| = 0\)?
5. How can inequalities involving absolute values be solved?

**Tip**: Always check whether the right-hand side of an absolute value equation is negative before solving—it can save you time!

Explore why the equation |x - 1| = -6 has no real solution, highlighting key algebraic concepts and the properties of absolute values. This detailed solution is suitable for students in Grades 8-10.

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