Final answer:
After equating the expressions for opposite sides of the parallelogram (2x + 10 and 5x - 20) and solving for x, we substitute the value of x into the expression for the side length (4x - 1) and determine that the side length is 39 units. However, this answer is not represented in the given options, indicating an error in the question or options.
Step-by-step explanation:
To find the length of the side of the parallelogram represented by 4x - 1, we first need to recognize that the opposite sides of a parallelogram are equal in length. Based on the question, we have sides of length 2x + 10 and 5x - 20. Hence, these expressions must be equal to each other because they represent the lengths of opposite sides. Setting them equal gives us:
2x + 10 = 5x - 20
To solve for x, we subtract 2x from both sides of the equation:
2x + 10 - 2x = 5x - 20 - 2x
10 = 3x - 20
Now we add 20 to both sides:
10 + 20 = 3x - 20 + 20
30 = 3x
Dividing both sides by 3 gives us the value of x:
30 / 3 = 3x / 3
x = 10
With x found, we can now determine the length of the side represented by 4x - 1:
4x - 1 = 4(10) - 1
4x - 1 = 40 - 1
4x - 1 = 39
Therefore, the correct length of the side is 39 units, which is not represented by any of the options provided in A) 9x−10 B) 11x−30 C) 7x−10 D) 6x−19. Thus, there appears to be an error in the question or the given options. The calculated length of the side does not match any of the provided choices.