The equation given is:

\[
|x| = 11
\]

This equation represents the absolute value of \( x \). The absolute value of a number is always non-negative, meaning it represents the distance of that number from 0 on the number line, regardless of direction.

To solve the equation \( |x| = 11 \), we consider both possible cases:

1. **Case 1:** \( x \) is positive or zero:
   \[
   x = 11
   \]

2. **Case 2:** \( x \) is negative:
   \[
   x = -11
   \]

So, the two possible solutions for the equation \( |x| = 11 \) are:

\[
x = 11 \quad \text{or} \quad x = -11
\]

Would you like more details or have any questions about this solution?

### Related Questions:
1. How does the absolute value function work for different types of numbers?
2. Can an absolute value equation have more than two solutions?
3. How do you solve absolute value inequalities?
4. What happens if the equation was \( |x| = -11 \)?
5. How do you graph the equation \( |x| = 11 \) on a number line?
6. What are the properties of absolute values that are useful in solving equations?
7. How does adding or subtracting a number inside the absolute value affect the solution?
8. How do absolute values relate to distance on the coordinate plane?

**Tip:** When solving absolute value equations, always remember to consider both the positive and negative scenarios.

Learn how to solve the absolute value equation |x| = 11 with a detailed step-by-step solution. Understand the concept of absolute value and its applications in equations. Suitable for students in Grades 7-9.

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