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The problem asks to find the value of \( x \), given that the square and equilateral triangle have the same perimeter. 

### Step-by-step solution:

1. **Square Perimeter**:
   Each side of the square is given as \( 2x - 3 \). Since a square has four equal sides, the perimeter of the square is:
   \[
   P_{\text{square}} = 4(2x - 3) = 8x - 12
   \]

2. **Equilateral Triangle Perimeter**:
   Each side of the equilateral triangle is given as \( 2x - 2 \). Since an equilateral triangle has three equal sides, its perimeter is:
   \[
   P_{\text{triangle}} = 3(2x - 2) = 6x - 6
   \]

3. **Set the Perimeters Equal**:
   We know that the perimeters of the square and the triangle are equal, so:
   \[
   8x - 12 = 6x - 6
   \]

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

### Final Answer:
The value of \( x \) is \( 3 \).

Would you like further details or explanations?

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Here are some related questions:
1. What would happen if the square had different side lengths?
2. How can you check if your value of \( x \) is correct by using the perimeter?
3. How do perimeters change when a figure’s side lengths involve variables?
4. What are other properties of an equilateral triangle besides equal sides?
5. How do you find the area of both shapes given the value of \( x \)?

**Tip:** Always recheck your algebraic steps, especially when solving equations with variables on both sides!

The square and equilateral triangle have the same perimeter. The square has side lengths 2x - 3, and the triangle has side lengths 2x - 2. Find the value of x.

This problem involves finding the value of x when a square and an equilateral triangle have the same perimeter. Using algebraic equations, learn how to solve for x when side lengths are expressed as variables.

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