Final answer:
The numerical length of TU is determined by setting up an equation where SU equals the sum of ST and TU and solving for x. The correct length of TU, after solving the equation, is 7 units.
Step-by-step explanation:
The question is asking to determine the numerical length of the line segment TU given two algebraic expressions for the lengths of line segments SU and TU, where point T lies on line segment SU. Since the total length of SU is the sum of the lengths of ST and TU, and SU is represented by the expression x+7, we can deduce that the length of ST must be equal to x. As TU is given by the expression 2x-1, we can set up an equation where the sum of ST and TU equals SU:
x + (2x-1) = x+7
Solving the equation:
3x - 1 = x + 7
2x = 8
x = 4
Then we plug x = 4 into the expression for TU (2x-1) to find the length:
TU = 2(4) - 1 = 8 - 1 = 7
Thus, the numerical length of TU is 7 units, which corresponds to option D.