Given that \( x \geq 0 \), we need to find the value of \( |-x| \).

First, let's recall the definition of absolute value. The absolute value of a number \( y \), denoted \( |y| \), is defined as:

\[ |y| = \begin{cases} 
y & \text{if } y \geq 0 \\
-y & \text{if } y < 0 
\end{cases} \]

In this problem, we are dealing with \( |-x| \). We know that \( x \geq 0 \). Let's analyze \( -x \):

- Since \( x \geq 0 \), it follows that \( -x \leq 0 \).

Now, apply the definition of absolute value to \( -x \):

\[ |-x| = \begin{cases} 
-x & \text{if } -x \geq 0 \\
-(-x) = x & \text{if } -x < 0 
\end{cases} \]

Given \( -x \leq 0 \), it means \( -x < 0 \) (unless \( x = 0 \) in which case \( -x = 0 \)). Therefore, we use the second case of the absolute value definition:

\[ |-x| = -(-x) = x \]

So, for \( x \geq 0 \), the value of \( |-x| \) is \( x \).

### Summary:
\[ |-x| = x \quad \text{for} \quad x \geq 0 \]

Would you like more details or have any questions?

### Related Questions:
1. What is the absolute value of \( x \) when \( x < 0 \)?
2. How does the absolute value function behave on the entire set of real numbers?
3. Can you prove the absolute value properties algebraically?
4. What is the geometric interpretation of absolute value on a number line?
5. How do you solve equations involving absolute values?
6. What are the differences between the absolute value function and the modulus function?
7. How can absolute values be applied in real-world scenarios?
8. What is the significance of the absolute value in complex numbers?

### Tip:
When dealing with absolute values, always consider the sign of the number inside the absolute value to apply the correct definition.

Explore the concept of absolute value with a focus on understanding the expression |-x| where x is non-negative. Learn how to apply the absolute value definition and its implications. Suitable for students in Grades 7-9.

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