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.