Final Answer:
The midpoint of the line segment 3x - 31 and x + 6 is B = (2x - 12).
Step-by-step explanation:
In geometry, the midpoint of a line segment is calculated by finding the average of the x-coordinates and the y-coordinates of the two endpoints.
For the given line segment with endpoints represented by 3x - 31 and x + 6, the x-coordinate of the midpoint (B) is found by averaging the x-coordinates:
[ B_x = frac{(3x - 31) + (x + 6)}{2} ]
Simplifying the expression gives the x-coordinate of the midpoint as (2x - 12).
This result signifies that the x-coordinate of the midpoint B is obtained by adding the x-coordinates of the endpoints and dividing by 2.
Therefore, the final answer is B = (2x - 12).