Firstly, we need to remember the segment addition postulate in geometry. According to the postulate, if a point N is situated on the segment MO, the whole segment MO equals the sum of the two smaller segments MN and NO.
It is given that NO = 2x - 3, MO = 3x + 5, and MN = 2x + 3.
So, according to the segment addition postulate, we can write this relationship as MO = MN + NO.
That means, 3x + 5 = (2x + 3) + (2x - 3).
Now, we just need to solve this equation for x to determine its value: After simplification, we find that x = 5.
Finally, we substitute x = 5 into the expression for MO to determine the length of the segment MO.
Plugging x = 5 into MO = 3x + 5 gives MO = 3*5 + 5 = 15 + 5 = 20.
So, the length of the line segment MO ‾ is 20 units.