The equation \(|x - 1| = -2\) has no solution. This is because the absolute value of a number is always non-negative (i.e., greater than or equal to zero). It can never be negative, like \(-2\).

### Explanation:
1. The absolute value of any expression, such as \(|x - 1|\), represents the distance of that expression from zero, which is always zero or positive.
2. Since no value of \(x\) can make \(|x - 1|\) equal to \(-2\), there are no \(x\)-values to graph.

Therefore, there is no graph for this equation as it has no real solutions.

### Questions for Further Exploration:
1. What are the properties of absolute value functions?
2. How do you solve absolute value equations like \(|x + 3| = 5\)?
3. What is the graphical interpretation of an absolute value function?
4. How can you graph absolute value inequalities?
5. What happens if you change \(|x - 1| = -2\) to \(|x - 1| = 2\)?

**Tip:** Absolute value equations can only have real solutions when set equal to a non-negative value.

Understand why the equation |x - 1| = -2 has no solution, as absolute values are always non-negative. Explore key concepts of absolute value equations, and learn more about why this equation cannot be graphed. Suitable for Grades 7-9 students.

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