1. The problem states that the length of one side of a square frame is $3x - 7$. 2. We need to find the perimeter of the square. The perimeter $P$ of a square with side length $s$ is given by the formula: $$P = 4s$$ 3. Since the side length is $3x - 7$, substitute this into the formula: $$P = 4(3x - 7)$$ 4. This expression can also be written as the sum of all four sides: $$(3x - 7) + (3x - 7) + (3x - 7) + (3x - 7)$$ 5. The expression $4(3x) + 4(-7)$ is equivalent to $4(3x - 7)$ by the distributive property: $$4(3x - 7) = 4 \times 3x + 4 \times (-7) = 4(3x) + 4(-7)$$ 6. The expression $(3x - 7)^4$ is not the perimeter; it represents the side length raised to the fourth power, which is unrelated to perimeter. **Final answer:** The correct expressions for the perimeter are: - $4(3x - 7)$ - $(3x - 7) + (3x - 7) + (3x - 7) + (3x - 7)$ - $4(3x) + 4(-7)$ The expression $(3x - 7)^4$ is incorrect for perimeter.