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It looks like you have an assignment about finding the perimeter of a regular polygon. The problem involves solving an equation for the side length of the polygon, as shown by the triangle and given equations in the image.

To help you with this:

1. From the image, the triangle has three sides, which indicates it's an equilateral triangle (regular polygon with 3 sides). 
2. The equation given on the triangle's sides involves algebraic expressions for each side:
   - One side: \(5 - 2x\)
   - Another side: \( -4x + 9 \)
   
Since the triangle is regular (equilateral), all three sides must be equal. So, we can set the two expressions equal to each other:

\[
5 - 2x = -4x + 9
\]

### Solving the equation:
1. Add \(4x\) to both sides to eliminate \(x\) from the right side:
   \[
   5 + 2x = 9
   \]
2. Subtract 5 from both sides:
   \[
   2x = 4
   \]
3. Divide both sides by 2:
   \[
   x = 2
   \]

Now that we have \(x = 2\), we can substitute it back into either expression for the side length. Let’s substitute into the first expression:

\[
\text{Side length} = 5 - 2(2) = 5 - 4 = 1
\]

So, each side of the triangle is 1 unit.

### Perimeter:
For a regular polygon (in this case, a triangle), the perimeter is just the side length multiplied by the number of sides:

\[
\text{Perimeter} = 1 \times 3 = 3 \text{ units}
\]

Thus, the perimeter of the polygon is **3 units**.

---

Would you like more details or further clarifications?

Here are some related questions for practice:
1. How would you find the perimeter of a regular hexagon if one side is 5 units?
2. What is the formula for the perimeter of a regular polygon with \(n\) sides?
3. If one side of a square is represented by \(3x + 1\), how would you find the perimeter if \(x = 2\)?
4. How does the perimeter of a triangle change if one side length doubles?
5. What is the difference between perimeter and area for polygons?

**Tip:** Always double-check if a polygon is regular (all sides are equal) before applying the perimeter formula!

Find the perimeter of the regular polygon. Given expressions for side lengths are 5 - 2x and -4x + 9.

Learn how to find the perimeter of a regular polygon by solving for side length using algebraic expressions. This problem is suitable for students in Grades 6-8 and involves geometric and algebraic concepts.

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