Question

point n is on line segment \\(\overline{mo}\\). given \\(mo = 3x - 10\\), \\(no = x\\), and \\(mn = 8\\), determine the numerical length of \\(\overline{mo}\\).

Explanation:

Step1: Use segment addition postulate

Since \( N \) is on \( \overline{MO} \), we have \( MN + NO = MO \). Substituting the given values: \( 8 + x = 3x - 10 \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 8 = 2x - 10 \).
Add 10 to both sides: \( 18 = 2x \).
Divide by 2: \( x = 9 \).

Step3: Find \( MO \)

Substitute \( x = 9 \) into \( MO = 3x - 10 \): \( MO = 3(9) - 10 = 27 - 10 = 17 \).

Answer:

\( 17 \)