Question

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

Explanation:

Step1: Use segment - addition postulate

Since point N is on line segment $\overline{MO}$, we have $MN + NO=MO$. Substitute the given expressions: $(2x + 3)+(2x - 3)=3x + 5$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+2x+3 - 3=4x$. So the equation becomes $4x=3x + 5$.

Step3: Solve for x

Subtract $3x$ from both sides of the equation: $4x-3x=3x + 5-3x$. We get $x = 5$.

Step4: Find the length of MO

Substitute $x = 5$ into the expression for $MO$. Since $MO=3x + 5$, then $MO=3\times5+5$.
$MO=15 + 5=20$.

Answer:

$20$