The equation provided in the image is:

$|x - 1| = 4$

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

1. Positive case: $x - 1 = 4$

   • Solving for $x$: $x = 4 + 1 = 5$

2. Negative case: $x - 1 = -4$

   • Solving for $x$: $x = -4 + 1 = -3$

Therefore, the solutions for $x$ are: $x = 5 \quad \text{or} \quad x = -3$

Would you like more details or have any questions about this solution?

Here are some related questions:

1. What are the general steps to solve an absolute value equation?
2. How would the solution change if the equation were $|x - 1| \leq 4$?
3. How do you graph the solution $|x - 1| = 4$ on a number line?
4. What would happen if the absolute value equation was set equal to a negative number?
5. How does this method extend to more complex absolute value equations?

Tip: When solving absolute value equations, always consider both the positive and negative cases of the expression inside the absolute value.