The image presents four puzzles asking to find the perimeters of different rectangles, each with algebraic expressions for the side lengths. Here's how to approach each:

1. First Rectangle:

• Length: $3x + 2$

• Width: $2x$

  Perimeter formula: $P = 2 \times (\text{Length} + \text{Width}) = 2 \times ((3x + 2) + 2x)$ Simplifying: $P = 2 \times (5x + 2) = 10x + 4$ Perimeter: $10x + 4$

2. Second Rectangle:

• Length: $x$

• Width: $4x + 1$

  Perimeter formula: $P = 2 \times (x + (4x + 1))$ Simplifying: $P = 2 \times (5x + 1) = 10x + 2$ Perimeter: $10x + 2$

3. Third Rectangle:

• Length: $x + 5$

• Width: $7$

  Perimeter formula: $P = 2 \times ((x + 5) + 7)$ Simplifying: $P = 2 \times (x + 12) = 2x + 24$ Perimeter: $2x + 24$

4. Fourth Rectangle:

• Length: $4x - 3$

• Width: $5$

  Perimeter formula: $P = 2 \times ((4x - 3) + 5)$ Simplifying: $P = 2 \times (4x + 2) = 8x + 4$ Perimeter: $8x + 4$

Would you like any details on the steps or further explanations? Here are five questions to expand your learning:

1. How do you simplify expressions within parentheses when solving for the perimeter?
2. Can you explain why multiplying by 2 is necessary for the perimeter formula?
3. How would you solve these perimeter expressions if you were given a specific value for $x$?
4. What happens to the perimeter if you double the length and width expressions?
5. Can you calculate the area for any of these rectangles?

Tip: Always check if the algebraic expressions in a problem can be simplified before substituting values.