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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**.

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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.

Solve the given absolute value equations:
1. |x - 1| = 2
2. |2x - 4| = 4
3. |3 - 2x| = 5
4. |x - 2| = -1

Learn how to solve absolute value equations such as |x - 1| = 2, |2x - 4| = 4, and |3 - 2x| = 5, with detailed steps for each. Understand why |x - 2| = -1 has no solution due to the properties of absolute values. Suitable for Grades 7-9.

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