Final answer:
The numerical length of line segment MO is found by setting up the equation MN + NO = MO with the given values, solving for x, and then substituting x back into the expression for MO. The length of MO is 17 units.
Step-by-step explanation:
To determine the numerical length of line segment MO, we can use the given lengths of segments NO and MN. We're given that MO = 3x - 10, NO = x, and MN is stated to be 8 units. The sum of the lengths of segments MN and NO should equal the length of segment MO because point N is on MO.
So, we can write the equation:
MN + NO = MO. Substituting the given values we have:
8 + x = 3x - 10. To find the value of x, we rearrange the equation:
3x - x = 8 + 10, resulting in
2x = 18. Dividing both sides by 2 gives us:
x = 9.
Now that we have the value of x, we can substitute it into the expression for MO:
MO = 3(9) - 10, which simplifies to:
MO = 27 - 10, resulting in:
MO = 17.
Therefore, the numerical length of line segment MO is 17 units.