Question

point N is on line segment MO. Given MO = 3x + 6, NO = 5x, and MN = x, determine the numerical length of NO

Answer 1

To determine the numerical length of \( NO \), we first need to express the relationship among the segments \( MN \), \( NO \), and \( MO \). Given:

- \( MO = 3x + 6 \)
- \( NO = 5x \)
- \( MN = x \)

Since point \( N \) divides line segment \( MO \) into two segments, we have:

\[
MO = MN + NO
\]

Substituting the expressions we have into that equation:

\[
3x + 6 = x + 5x
\]

Simplifying the right side, we get:

\[
3x + 6 = 6x
\]

Now, to isolate \( x \), we can rearrange the equation:

\[
3x + 6 - 6x = 0
\]
\[
-3x + 6 = 0
\]
\[
6 = 3x
\]
\[
x = 2
\]

Next, we can substitute \( x = 2 \) into the expression for \( NO \):

\[
NO = 5x = 5(2) = 10
\]

Therefore, the numerical length of \( NO \) is:

\[
\boxed{10}
\]