The image you've uploaded contains a set of mathematical problems involving absolute values. Let's go through them one by one:

1. Problem 1: $|x - 1| = 2$ This absolute value equation can be broken down into two cases: $x - 1 = 2 \quad \text{or} \quad x - 1 = -2$ Solving these:

   • $x - 1 = 2$ → $x = 3$
   • $x - 1 = -2$ → $x = -1$

   Therefore, the solution is $x = 3$ or $x = -1$.

2. Problem 2: $|2x - 4| = 4$ Break into two cases: $2x - 4 = 4 \quad \text{or} \quad 2x - 4 = -4$ Solving these:

   • $2x - 4 = 4$ → $2x = 8$ → $x = 4$
   • $2x - 4 = -4$ → $2x = 0$ → $x = 0$

   So, the solution is $x = 4$ or $x = 0$.

3. Problem 3: $|3 - 2x| = 5$ Again, break into two cases: $3 - 2x = 5 \quad \text{or} \quad 3 - 2x = -5$ Solving these:

   • $3 - 2x = 5$ → $-2x = 2$ → $x = -1$
   • $3 - 2x = -5$ → $-2x = -8$ → $x = 4$

   Thus, the solution is $x = -1$ or $x = 4$.

4. Problem 4: $|x - 2| = -1$ Since the absolute value of any expression is always non-negative, it cannot equal a negative number. Therefore, this equation has no solution.

Would you like further details or explanations on any of the problems? Here are some related questions:

1. How do you solve absolute value inequalities?
2. Can an absolute value expression ever result in a negative number?
3. What are the general steps to solve absolute value equations?
4. How can we graph absolute value functions?
5. What are some real-world applications of absolute value equations?

Tip: Always check for extraneous solutions when dealing with absolute values, especially in equations that involve variables.