Solve inequality algrebrically and sketch solution on real number line question is |x-5|<0 

To solve the inequality \( |x - 5| < 0 \), we start by analyzing the properties of absolute values:

1. **Understand the absolute value inequality**: The absolute value of a number, \( |x - 5| \), represents the distance of \( x \) from 5 on the real number line. Since distance cannot be negative, \( |x - 5| \geq 0 \) for all real numbers \( x \).

2. **Interpretation**:
   - The inequality \( |x - 5| < 0 \) implies a requirement for the absolute value to be less than zero.
   - However, this is impossible because the absolute value is always non-negative (i.e., \( |x - 5| \geq 0 \)).

3. **Conclusion**: 
   - Since there is no value of \( x \) that can make \( |x - 5| < 0 \) true, the inequality has **no solution**.

### Solution on the Real Number Line
Since no values of \( x \) satisfy the inequality, there is no solution to represent on the real number line.

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Would you like further details or have any questions? 

Here are some related questions to deepen understanding:

1. What if the inequality was \( |x - 5| \leq 0 \)? 
2. How would the solution change if we had \( |x - 5| < 3 \) instead?
3. What does the inequality \( |x - 5| > 0 \) imply about the values of \( x \)?
4. How can inequalities involving absolute values be solved when they have non-zero constants?
5. How do we solve inequalities like \( |x - 5| \geq 2 \) on a number line?

**Tip**: Remember, the absolute value of any expression is always non-negative, so inequalities with negative values for absolute terms often have no solutions.

Solve inequality algebraically and sketch solution on real number line question is |x-5|<0

Understand why the inequality |x - 5| < 0 has no solution by analyzing absolute values and inequalities. This detailed explanation is suitable for students in Grades 9-11 and clarifies absolute value properties and inequalities on the real number line.

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