Question

point n is on line segment $overline{mo}$. given $mo = 3x + 6$, $no = 5x$, and $mn = x$, determine the numerical length of $overline{no}$.

Explanation:

Step1: Use segment - addition postulate

Since point N is on line segment $\overline{MO}$, we have $MO=MN + NO$. Substituting the given expressions: $3x + 6=x + 5x$.

Step2: Simplify the equation

Combine like - terms on the right - hand side: $3x+6 = 6x$.

Step3: Solve for x

Subtract $3x$ from both sides of the equation: $6=6x - 3x$, which simplifies to $3x = 6$. Then divide both sides by 3, so $x = 2$.

Step4: Find the length of $\overline{NO}$

Substitute $x = 2$ into the expression for $NO$. Since $NO = 5x$, then $NO=5\times2=10$.

Answer:

10