Question

question
point n is on line segment $overline{mo}$. given $mo = 3x + 6$, $no = 5x$, and $mn = x$, determine the numerical length of $overline{no}$.
answer attempt 1 out of 2
$no=$

Explanation:

Step1: Use segment - addition postulate

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

Step2: Simplify the left - hand side

Combining like terms on the left - hand side of the equation $x + 5x=3x + 6$, we get $6x=3x + 6$.

Step3: Isolate the variable $x$

Subtract $3x$ from both sides of the equation $6x=3x + 6$. So, $6x-3x=3x + 6-3x$, which simplifies to $3x=6$.

Step4: Solve for $x$

Divide both sides of the equation $3x = 6$ by 3. We have $\frac{3x}{3}=\frac{6}{3}$, so $x = 2$.

Step5: Find the length of $\overline{NO}$

We know that $NO = 5x$. Substitute $x = 2$ into the expression for $NO$. Then $NO=5\times2 = 10$.

Answer:

$10$