Final answer:
To find the length of segment AB, we use the given expressions AB = 2x - 15, BC = 3x + 3, and the given total length AC = 48, setting up the equation AB + BC = AC. Upon solving for x and plugging back into AB we find that the length of AB is 9 units.
Step-by-step explanation:
To find the length of segment AB when B is between A and C, we are given the following information: AB = 2x - 15, BC = 3x + 3, and AC = 48. Since B is between A and C, we can add AB and BC to get AC. Thus:
AB + BC = AC
(2x - 15) + (3x + 3) = 48
Combine like terms to get:
5x - 12 = 48
Add 12 to both sides:
5x = 60
Divide by 5:
x = 12
Now, substitute x back into the expression for AB:
AB = 2x - 15
AB = 2(12) - 15
AB = 24 - 15
AB = 9
Therefore, the length of AB is 9 units.