https://file.aiquickdraw.com/mathbot/file/1728336947037ydhxb626.jpg

The task shown in the image asks you to write two expressions for the perimeter of a polygon and simplify them.

### Step-by-Step Explanation:

1. **Identifying the side lengths**: 
   The figure is a pentagon with the side lengths labeled as:
   - 8
   - 2
   - 7x
   - 4x
   - 4

2. **Part (a): Writing the expression for the perimeter**:
   To find the perimeter of any polygon, we simply add all the side lengths together. So, the perimeter expression using all five side lengths is:
   \[
   \text{Perimeter} = 8 + 2 + 7x + 4x + 4
   \]

3. **Part (b): Simplifying the expression**:
   Combine like terms in the above expression:
   - The constants are: \( 8 + 2 + 4 = 14 \)
   - The variable terms are: \( 7x + 4x = 11x \)

   Therefore, the simplified expression for the perimeter is:
   \[
   \text{Perimeter} = 11x + 14
   \]

Would you like further details or explanations? Here are some related questions to expand your understanding:

1. How do you calculate the perimeter of a regular polygon?
2. What steps are involved in simplifying algebraic expressions with variables?
3. Can the variable \(x\) represent a specific value in this perimeter equation?
4. How do you solve for \(x\) if you know the perimeter of this polygon?
5. How do you interpret a variable in geometry problems involving polygons?

**Tip**: When solving algebraic expressions involving both constants and variables, always group similar terms (constants together and variable terms together) for simplification.

Write two expressions for the perimeter of the figure.

Learn how to write and simplify algebraic expressions for the perimeter of a pentagon. This problem involves adding side lengths and simplifying expressions. Suitable for students in Grades 6-8, covering core concepts of algebra and geometry.

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