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The image shows a series of exercises involving solving absolute value equations and graphing the solution sets on a number line. Here's an overview of how to approach these types of problems:

### For Absolute Value Equations:

1. **General Rule**: 
   - If \(|x - a| = b\), this means \(x - a = b\) **or** \(x - a = -b\).
   - Solve both equations to find the values of \(x\).

### Example Breakdown of Solutions:

1. **Problem 1:**
   - \(|x - 3| = 5\)
     - \(x - 3 = 5\) → \(x = 8\)
     - \(x - 3 = -5\) → \(x = -2\)
   - Graph: A number line showing two points: \(x = -2\) and \(x = 8\).

2. **Problem 2:**
   - \(|x + 4| = 9\)
     - \(x + 4 = 9\) → \(x = 5\)
     - \(x + 4 = -9\) → \(x = -13\)
   - Graph: Points at \(x = -13\) and \(x = 5\).

Each problem follows a similar pattern where you isolate the absolute value, split it into two equations, and solve both.

Would you like me to provide a step-by-step solution for each equation or assist with specific questions? Also, here are 5 related questions for practice:

1. How do you solve \(|x - 2| = 7\)?
2. What is the general process for graphing solutions on a number line?
3. How would the equation \(|2x + 3| = 8\) be solved?
4. What happens if the right-hand side of an absolute value equation is negative, such as \(|x - 1| = -3\)?
5. How can you write an absolute value equation given a number line with solution points?

**Tip**: Always check if the equation has a real solution. If the absolute value equals a negative number, there are no solutions.

Solve each equation and graph the solution set for absolute value equations.

Learn how to solve absolute value equations such as |x - 3| = 5 and graph the solutions on a number line. This problem covers key concepts including solving absolute value equations, graphing solution sets, and interpreting absolute value properties.

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