Final answer:
To find the numerical length of MN using the Segment Addition Postulate, we solve the equation 2x + (x - 2) = 2x + 9 to get x = 11, and then substitute into MN = 2x to conclude that MN = 22.
Step-by-step explanation:
The question requires the use of the Segment Addition Postulate, which states that if point N is between points M and O, then the segment MN plus segment NO equals the segment MO. Given MN equals twice NO (2 × NO), MN can be written as 2x, and NO as x - 2. The whole segment MO is given as 2x + 9.
So according to the Segment Addition Postulate, we combine MN and NO to equal MO, resulting in an equation: 2x + (x - 2) = 2x + 9. Solving this equation for x, we get:
3x - 2 = 2x + 9
3x - 2x = 9 + 2
Once we have x, we can find MN by substituting x back into MN = 2x, so:
MN = 2×(11)
MN = 22
Therefore, the numerical length of MN is 22.