Final answer:
The length of segment JM, given that M is the midpoint of JK, is found to be 40 units after solving the equation 7x + 5 = 8x.
Step-by-step explanation:
We are given that M is the midpoint of segment JK and the lengths of the segments are JM = 7x + 5 and MK = 8x. Since M is the midpoint, the lengths of JM and MK must be equal. Therefore, we can set up the equation 7x + 5 = 8x. To solve for x, subtract 7x from both sides to get 5 = x. Now that we have determined that x = 5, we can find the length of JM. Since JM = 7x + 5, substitute 5 for x to get JM = 7(5) + 5 = 35 + 5 = 40. Thus, the length of segment JM is 40 units.