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.