https://file.aiquickdraw.com/mathbot/file/1727057544648g7ltjwy6.jpg

The inequality given in the problem is:

\[
|k - 3| < -1
\]

### Explanation:

The absolute value of any expression, like \(|k - 3|\), represents the distance of the number \(k - 3\) from 0, and distance is always non-negative. Therefore, the absolute value function always results in a number that is greater than or equal to 0.

However, the inequality requires that \(|k - 3|\) is strictly less than \(-1\), which is impossible because absolute values can never be negative.

### Conclusion:
Since it is impossible for an absolute value to be less than a negative number, this inequality has **no solution**.

This is why the answer "no solution" is correct.

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Would you like further details or have any questions about this? Here are some additional questions related to absolute value inequalities:

1. How do you solve absolute value inequalities like \(|x - 5| < 4\)?
2. What are the general rules for solving \(|x - a| < b\) and \(|x - a| > b\)?
3. Can you explain how the graph of an absolute value function looks?
4. What happens when you solve \(|x - 3| > 0\)?
5. How does the inequality \(|x - 2| \geq 5\) compare to the one in this problem?

**Tip:** Always remember that an absolute value expression is always non-negative, so it can't be less than a negative number.

Solve the inequality: |k - 3| < -1. Graph the solution, if possible.

Understand why the inequality |k - 3| < -1 has no solution. The problem demonstrates key concepts of absolute values and inequalities, suitable for students in Grades 8-10.

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