https://file.aiquickdraw.com/mathbot/file/1726111976762sp7zods9.jpg

The equation in the image is:

\[
|2x| = 16
\]

To solve this absolute value equation, we break it into two cases:

1. **Positive case:**
   \[
   2x = 16
   \]
   Solving for \(x\):
   \[
   x = \frac{16}{2} = 8
   \]

2. **Negative case:**
   \[
   2x = -16
   \]
   Solving for \(x\):
   \[
   x = \frac{-16}{2} = -8
   \]

Thus, the solutions are \(x = 8\) and \(x = -8\), which can be written as:

\[
x = \pm 8
\]

So, the correct answer is \(\pm 8\), which corresponds to the first option in the image.

Do you want further details or have any questions? Here are five related questions to deepen understanding:

1. How do you solve general absolute value equations?
2. What is the geometric meaning of an absolute value equation?
3. Can absolute value equations have no solutions?
4. How would the solution change if the equation was \(|2x| = -16\)?
5. How do you graph absolute value functions?

**Tip:** Always remember that absolute value equations can result in two cases: one positive and one negative.

Learn how to solve the absolute value equation |2x| = 16 with detailed steps. This problem explores the concept of absolute value, providing solutions for both the positive and negative cases. Suitable for students in Grades 9-10.

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