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M is between S and H. Given that SM = 2x + 5, MH = 9x - 7, and SH = 86, determine the value of x.

A. x = 6
B. x = 7
C. x = 8
D. x = 9

1 Answer

2 votes

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:

  1. Add 2 to both sides: 11x - 2 + 2 = 86 + 2
  2. Simplify: 11x = 88
  3. Divide both sides by 11: x = 88 / 11
  4. Find the solution: x = 8

Therefore, the value of x is 8, which corresponds to answer choice C.

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