Final answer:
The value of x is found to be 12 by solving the equation 5x - 12 = 48. Subsequently, substituting x back into the expression for AB gives us AB = 9.
Step-by-step explanation:
The student is asking to solve for the value of AB, given that B is between A and C with AB and BC represented in terms of a variable x and the total distance AC known. From the question, we have AB = 2x - 15, BC = 3x + 3, and AC = 48. To find the value of AB, we first need to determine the value of x. Since AB+BC=AC, we can set up the equation 2x - 15 + 3x + 3 = 48. Solving this, we combine like terms to get 5x - 12 = 48. Adding 12 to each side gives us 5x = 60, and dividing each side by 5, we find that x = 12. Now, we can substitute x back into the expression for AB, which gives us AB = 2(12) - 15 = 24 - 15 = 9.