Final answer:
The student's problem involves finding the length of CT given the lengths of CA and AT, and the position of A. The solution requires setting up an equation based on the sum of segments, solving for the variable x, and substituting back to find the final length of CT.
Step-by-step explanation:
The student is asked to find the length of CT given that A is between C & T. The given lengths are CA = x-2, AT = 2x-4, and CT = 2x+1. To solve this, we use the fact that the length of CT is the sum of the lengths of CA and AT (because A is between C & T). So, we have the equation: CT = CA + AT. Substituting the given expressions, we get CT = (x-2) + (2x-4). Simplifying this, we get CT = 3x - 6. But the problem also tells us that CT = 2x + 1. So we can set up an equation: 3x - 6 = 2x + 1. Solving for x, we subtract 2x from both sides to get x - 6 = 1, and then add 6 to both sides to find x = 7. Finally, we substitute x back into the expression for CT to find the length: 2x + 1 = 2(7) + 1 = 14 + 1 = 15. Therefore, the length of CT is 15 units, which is not an option among the provided choices, indicating a possible error in the question or the options provided.