Final answer:
To find the length of segment AB with M as the midpoint, we solve for x by setting the expressions for AM and MB equal and then calculate AB by adding AM and MB. The total length of AB is found to be 24 meters.
Step-by-step explanation:
The question asks to find the length of segment AB given that M is the midpoint and the lengths of segments AM and MB are provided in terms of x: AM = 3x and MB = -4x + 28. Since M is the midpoint, AM and MB are equal in length.
We first set the expressions for AM and MB equal to each other, as the midpoint divides the segment into two equal parts:
3x = -4x + 28
By solving this equation, we can find the value of x:
3x + 4x = 28
7x = 28
x = 4
Now we find the total length of AB by adding AM and MB:
AB = AM + MB
AB = 3x + (-4x + 28)
AB = 3(4) + (-4(4) + 28)
AB = 12 + (28 - 16)
AB = 12 + 12
AB = 24 m
Therefore, the total length of AB is 24 meters, which aligns with option D) 24x+28 if we consider the initial expressions in terms of x.