Final answer:
To solve for x, set the expressions for TS and SV equal due to S being the midpoint of TV, and then simplify the resulting equation. The result is x = 8.
Step-by-step explanation:
The student is given that S is the midpoint of segment TV, hence TS equals SV. They are provided with two equations for these lengths, TS = 4x - 7 and SV = 5x - 15. To find the value of x, we must set these two expressions equal to each other because the midpoint implies both segments are of equal length.
- Set TS equal to SV: 4x - 7 = 5x - 15.
- Solve for x: Add 7 to both sides to get 4x = 5x - 8, and then subtract 5x from both sides to find that x = 8.