We are given the equation:

$2|x - 1| = 8$

Step 1: Isolate the absolute value expression

First, divide both sides by 2 to isolate the absolute value expression:

$|x - 1| = \frac{8}{2}$

$|x - 1| = 4$

Step 2: Solve for the two cases

The absolute value equation $|x - 1| = 4$ means that $x - 1$ can either be 4 or -4. Therefore, we have two cases to solve:

Case 1: $x - 1 = 4$

Solve for $x$:

$x = 4 + 1 = 5$

Case 2: $x - 1 = -4$

Solve for $x$:

$x = -4 + 1 = -3$

Step 3: Conclusion

The two solutions to the equation $2|x - 1| = 8$ are:

$x = 5 \quad \text{and} \quad x = -3$

Thus, there are 2 solutions to the equation.

---

Would you like further details or have any questions? Here are some related questions to explore:

1. How would the solutions change if the equation were $3|x - 2| = 12$?
2. What is the general method to solve absolute value equations of the form $a|x - b| = c$?
3. How can you solve absolute value inequalities such as $|x - 3| \leq 5$?
4. What happens if the absolute value equation includes a negative sign inside, like $|x - 1| = -4$?
5. Can absolute value equations have no solutions? If so, when?

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