The equation in the image is:

$|4x| + 5 = 13$

Step 1: Isolate the absolute value term

$|4x| = 13 - 5$ $|4x| = 8$

Step 2: Solve for $4x$ in both cases (absolute value equation splits into two cases)

1. $4x = 8$ $x = \frac{8}{4} = 2$

2. $4x = -8$ $x = \frac{-8}{4} = -2$

Final Answer:

The solutions are: $x = 2 \quad \text{or} \quad x = -2$

Let me know if you'd like further details or have questions!

Here are 5 related questions to expand your understanding:

1. How would you solve $|5x| + 7 = 22$?
2. What happens if the right-hand side of the equation is negative?
3. How do absolute value inequalities differ from equations?
4. Can you generalize the steps to solve any absolute value equation?
5. What if the absolute value expression contains more complex terms, like $|2x - 3|$?

Tip: When solving absolute value equations, always remember to check both positive and negative cases!