The equation in the image is:

$|2x + 4| = 8$

To solve this absolute value equation, follow these steps:

Step 1: Set up two separate cases since the absolute value expression can be either positive or negative.

Case 1:

$2x + 4 = 8$ Solve for $x$: $2x = 8 - 4$ $2x = 4$ $x = 2$

Case 2:

$2x + 4 = -8$ Solve for $x$: $2x = -8 - 4$ $2x = -12$ $x = -6$

Final Answer:

The solutions are $x = 2$ and $x = -6$.

Conclusion:

The correct option is the one that shows $x = 2$ and $x = -6$.

Do you need more details or have any questions?

Related Questions:

1. How do you solve absolute value inequalities?
2. What happens if there is no solution for an absolute value equation?
3. Can you explain how to graph absolute value functions?
4. What is the difference between an absolute value equation and an absolute value inequality?
5. How do you check the solutions for absolute value equations?

Tip:

When solving absolute value equations, always check for both positive and negative cases!