Final answer:
In this segment addition problem, the lengths SM, MH, and SH are provided, and the equation 11x - 2 = 86 leads to the solution x = 8, corresponding to answer choice C.
Step-by-step explanation:
The student is asked to find the value of x in a segment addition problem where M is between S and H. We're given the lengths in terms of x: SM = 2x + 5, MH = 9x - 7, and the total length SH = 86. To find the value of x, we need to set up the equation 2x + 5 + 9x - 7 = 86, which simplifies to 11x - 2 = 86. By solving this equation, we can find the value of x that will make the equation true.
The equation simplifies to:
- Add 2 to both sides: 11x - 2 + 2 = 86 + 2
- Simplify: 11x = 88
- Divide both sides by 11: x = 88 / 11
- Find the solution: x = 8
Therefore, the value of x is 8, which corresponds to answer choice C.