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.