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The problem presents a square with side lengths labeled as expressions. We are tasked to find the value of \(x\).

### Given information:
- One side of the square (e.g., \( AB \)) is labeled \( 3x + 4 \).
- The opposite side (e.g., \( BC \)) is labeled \( 9x - 8 \).

### Approach:
Since the figure is a square, all sides must be equal. Therefore, we can set the two expressions for the sides equal to each other and solve for \(x\).

\[
3x + 4 = 9x - 8
\]

### Step 1: Solve for \(x\)
1. Subtract \(3x\) from both sides:
   \[
   4 = 6x - 8
   \]
2. Add 8 to both sides:
   \[
   12 = 6x
   \]
3. Divide by 6:
   \[
   x = 2
   \]

Thus, the value of \(x\) is \( \boxed{2} \).

Would you like more details or have any further questions?

Here are some related questions to consider:
1. What would happen if the figure was not a square but a rectangle?
2. How can we check that the solution for \(x = 2\) is correct?
3. What is the length of each side of the square when \(x = 2\)?
4. What if a different pair of sides were given? Would the process change?
5. How do you solve for \(x\) if more complex expressions were given for the sides?

**Tip:** Whenever solving for \(x\) in geometry problems involving squares or rectangles, remember that equality of sides is key to setting up equations.

The figure is a square. Find the value of x, where one side is represented as 3x + 4 and the other as 9x - 8.

Learn how to solve for x in a square where the side lengths are given by the expressions 3x + 4 and 9x - 8. This solution involves algebraic manipulation and the equality of sides in a square. Suitable for students in Grades 7-9.

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