The equation shown in the image is:

$|x - 2| + 5 = 9$

To solve this, let's follow these steps:

Step 1: Isolate the absolute value

First, subtract 5 from both sides of the equation:

$|x - 2| = 9 - 5$ $|x - 2| = 4$

Step 2: Solve the absolute value equation

Now that we have $|x - 2| = 4$, this means:

1. $x - 2 = 4$
2. $x - 2 = -4$

Step 3: Solve both equations

For $x - 2 = 4$: $x = 4 + 2 = 6$

For $x - 2 = -4$: $x = -4 + 2 = -2$

Final Answer:

The solutions are: $x = 6 \quad \text{or} \quad x = -2$

Would you like more details or have any questions?

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Here are some related questions you might find useful:

1. How do we handle more complex absolute value equations?
2. Can this method be extended to inequalities involving absolute values?
3. How does graphing $|x - 2|$ help in understanding this solution?
4. What if the absolute value equation has no solution?
5. How does solving an absolute value equation differ from solving linear equations?

Tip: Always remember to check both positive and negative cases when solving absolute value equations.