Let's focus on **Case 2** of the equation \( |2x| = 8 \):

### Case 2: \( 2x = -8 \)

In this case, we solve for \( x \) as follows:

1. **Start with the equation**:
   \[
   2x = -8
   \]

2. **Solve for \( x \)**:
   \[
   x = \frac{-8}{2}
   \]
   \[
   x = -4
   \]

### Verification:
To ensure that this solution is correct, let's substitute \( x = -4 \) back into the original equation \( |2x| - 3 = 5 \):

1. **Calculate \( 2x \)**:
   \[
   2(-4) = -8
   \]

2. **Find the absolute value**:
   \[
   |2x| = |-8| = 8
   \]

3. **Substitute into the original equation**:
   \[
   |2x| - 3 = 8 - 3 = 5
   \]
   This confirms that the left-hand side equals the right-hand side.

Thus, the solution \( x = -4 \) is correct for Case 2.

Would you like to see more details or have any questions?

Here are five related questions to consider:

1. How would the solution change if the equation were \( |3x| - 3 = 5 \)?
2. Can you explain why we must consider both positive and negative scenarios in absolute value equations?
3. What if the equation were \( |2x| - 3 = -5 \)? Would there be any solutions?
4. How do you interpret the solutions \( x = 4 \) and \( x = -4 \) on a number line?
5. How would you set up an equation if the original problem involved \( |2x + 1| = 8 \)?

**Tip**: Always check your solutions by substituting them back into the original equation to ensure they satisfy all conditions.

Learn how to solve the absolute value equation |2x| = 8 step-by-step. Verify the solution x = -4 by substituting it back into the original equation |2x| - 3 = 5. This problem covers key concepts in absolute value equations and is suitable for students in Grades 9-12.

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