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The expression \( \left| a - 2 - \sqrt{(a - 1)^2} \right| \) for \( a < 0 \) simplifies to:

\[
\left| -a + \left| a - 1 \right| + 2 \right|
\]

Would you like a more detailed breakdown of this solution?

Here are 5 related questions that could expand your understanding:

1. How does the absolute value function affect the result for different values of \( a \)?
2. What happens if \( a \geq 0 \)? How would the expression simplify in that case?
3. What is the geometric interpretation of absolute values and square roots in this context?
4. How does the expression change if \( \sqrt{(a - 1)^2} \) is expanded explicitly?
5. How do we handle expressions inside absolute value functions when solving inequalities?

**Tip**: When simplifying expressions with square roots and absolute values, consider the sign of the variable inside the square root.

Which expression is equal to |a - 2 - √(a - 1)^2| for a < 0?

Learn how to simplify the expression |a - 2 - √(a - 1)^2| for values of a less than 0. This problem involves algebraic concepts such as absolute value, square roots, and simplification techniques. Suitable for high school students in Grades 9-12.

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