Question

find mo if n is between m and o.
mn = 2x + 3, mo = 5x + 8, no = 4x - 4
(you should draw and work this out on paper before answering.)

Explanation:

Step1: Apply segment - addition postulate

Since $N$ is between $M$ and $O$, we have $MN + NO=MO$. Substitute the given expressions: $(2x + 3)+(4x - 4)=5x + 8$.

Step2: Simplify the left - hand side

Combine like terms: $2x+4x+3 - 4=6x - 1$. So, $6x - 1=5x + 8$.

Step3: Solve for $x$

Subtract $5x$ from both sides: $6x-5x-1=5x - 5x+8$, which gives $x-1 = 8$. Then add 1 to both sides: $x=9$.

Step4: Find $MO$

Substitute $x = 9$ into the expression for $MO$. Since $MO=5x + 8$, then $MO=5\times9+8$. Calculate $5\times9+8=45 + 8=53$.

Answer:

$53$