Final answer:
To find the length XZ, set up an equation with XM and MZ. Solve the equation to find the value of x. Substitute the value of x back into XM to find the length of XZ.
Step-by-step explanation:
To find the length XZ, we can use the fact that M is the midpoint of the segment. This means that XM and MZ are equal in length. So, we can set up the equation 2x+35 = 5x-22 where 2x+35 represents XM and 5x-22 represents MZ. Now, we can solve this equation to find the value of x.
2x+35 = 5x-22
35 + 22 = 5x - 2x
57 = 3x
x = 57/3
x = 19
Now that we have found the value of x, we can substitute it back into either XM or MZ to find the length of XZ. Let's substitute it into XM:
XM = 2x+35 = 2(19)+35 = 38+35 = 73
Therefore, the length of XZ is 73.