https://file.aiquickdraw.com/mathbot/file/1726126717456mlncyffj.jpg

To solve this problem, let's break it down step by step.

The shape given in the image has expressions on each side, and we are asked to simplify the total perimeter of this polygon. The perimeter is the sum of all sides of the polygon, so we add up the expressions for each side.

The sides of the polygon are labeled as follows:
- Two sides are \( 2n + 3 \)
- Two sides are \( n \)
- One side is \( 3n - 4 \)

So, the expression for the perimeter \( P \) is:
\[
P = (2n + 3) + (2n + 3) + n + n + (3n - 4)
\]
Simplifying the expression:
\[
P = 2n + 3 + 2n + 3 + n + n + 3n - 4
\]
\[
P = (2n + 2n + n + n + 3n) + (3 + 3 - 4)
\]
\[
P = 9n + 2
\]

Now, substitute \( n = 14 \) into the simplified expression:
\[
P = 9(14) + 2 = 126 + 2 = 128
\]

So, the perimeter when \( n = 14 \) is 128. However, none of the given choices match this value, so it looks like there may be an error in the question or the provided answer options. The correct result is \( 128 \).

Let me know if you'd like further clarification or have any other questions!

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**Questions:**
1. What would happen if \( n = 0 \)? What would the perimeter be?
2. How would the result change if one of the expressions had a different constant, such as \( 2n + 5 \)?
3. What does the variable \( n \) represent in the context of this shape?
4. How do you interpret the expression \( 3n - 4 \) geometrically in the polygon?
5. Can this expression for perimeter be used for other polygons with different side expressions?

**Tip:** Always ensure you double-check the simplified form before substituting the value for \( n \).

Simplify the expression then evaluate it when n = 14. Choose the letter of the correct answer.

Learn how to simplify algebraic expressions and evaluate them for specific values. This problem involves finding the perimeter of a polygon by summing expressions for each side and substituting n = 14. Suitable for students in Grades 6-8.

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