Point N is on line segment MO. Given NO = 2x – 3, MO = 3x + 5, and MN = 2x + 3, determine the numerical length of MO.

MO = 20

Explanation:

Given that: MO = 3x + 5

                  MN = 2x + 3

                  NO = 2x - 3

But,

MO = MN + NO

So that;

3x + 5 = (2x + 3) + (2x - 3)

3x + 5 = 2x + 3 + 2x - 3

3x + 5 = 4x

3x - 4x = -5

-x = -5

Multiply through by minus,

x = 5

Thus,

MO = 3x + 5

      = 3(5) + 5

      = 15 + 5

MO = 20

The length of MO is 20.