Final answer:
To find the value of AM, set the lengths equal since M is the midpoint, solve the resulting equation to find x, and then substitute the value of x back into the expression for AM. The calculation shows AM = 29.
Step-by-step explanation:
The question is asking us to find the value of AM given that M is the midpoint of the segment AB and the lengths of AM and MB are given by 3x + 17 and 7x + 1 respectively. Since M is the midpoint, the lengths of AM and MB are equal, which means we can set them equal to each other to find the value of x:
3x + 17 = 7x + 1.
By solving this equation for x, we first subtract 3x from both sides, obtaining:
17 = 4x + 1.
Next, we subtract 1 from both sides to get:
16 = 4x.
Dividing both sides by 4 gives us:
x = 4.
Now that we have the value of x, we can substitute it back into the expression for AM to find the length:
AM = 3(4) + 17 = 12 + 17 = 29.
Therefore, the value of AM is not explicitly given in the options a) to d), but it should be calculated as part of the solution process.