Final answer:
After solving the equation based on the given values, it is found that the numerical length of MN should be 22 units, which is not listed among the provided options. This indicates a discrepancy in the question or answer choices.
Step-by-step explanation:
To determine the numerical length of MN, we must understand that the length of the entire line segment MO is the sum of its parts, MN and NO. Given that MN = 2×, NO = ×2 - 2, and MO = 2× + 9, we can create the equation:
MO = MN + NO
2× + 9 = 2× + (×2 - 2)
Now we solve for × using basic algebraic operations:
2× + 9 = 2× + × - 2
9 + 2 = × (combine like terms)
× = 11 (solving for ×)
With the value of ×, we can now calculate MN:
MN = 2×
MN = 2(11)
MN = 22
Therefore, the numerical length of MN is not one of the given options (a 6 units, b 9 units, c 12 units, d 15 units), indicating an error in either the problem statement or the provided options. Based on the calculations with the given values, MN should be 22 units.