Solve.
StartAbsoluteValue x EndAbsoluteValuexequals=11
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The​ solution(s) is/are enter your response here
​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)
B.
There is no solution.

The given equation is:

\[
|x| = 11
\]

The absolute value equation \( |x| = 11 \) implies two possible solutions, since the absolute value of a number is its distance from zero, regardless of the direction (positive or negative). Thus, we can write:

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

So, the solutions are:

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

### Final Answer:
A. The solutions are \( x = 11 \) and \( x = -11 \).

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Do you have any questions or need further clarification? Here are five related questions:

1. How would you solve \( |x| = 7 \)?
2. What if \( |x| = -5 \), would there be any solution?
3. Can you solve the inequality \( |x| \leq 12 \)?
4. How would you solve \( |x + 3| = 9 \)?
5. What does \( |x| \) represent geometrically?

**Tip:** Absolute value equations always result in two solutions, unless it's an inequality or negative value.

Solve |x| = 11. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Learn how to solve the absolute value equation |x| = 11. This problem explains key algebraic concepts and demonstrates how to find two solutions using the absolute value theorem. Suitable for students in Grades 6-8.

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