https://file.aiquickdraw.com/mathbot/file/1727112178977tegs5gtm.jpg

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.

Learn how to solve the absolute value equation |x - 2| + 5 = 9 with a step-by-step solution. This example highlights the key algebraic concepts of absolute values and equation solving. Suitable for students in Grades 7-9.

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