Question

question point m is on line segment $overline{ln}$. given $mn = 3x$, $ln = 4x + 9$, and $lm = 2x + 7$, determine the numerical length of $overline{lm}$.

Explanation:

Step1: Use segment - addition postulate

Since point M is on line segment $\overline{LN}$, we have $LM + MN=LN$. Substitute the given expressions: $(2x + 7)+3x=4x + 9$.

Step2: Combine like - terms on the left - hand side

$2x+3x + 7=4x + 9$, which simplifies to $5x+7 = 4x + 9$.

Step3: Solve for x

Subtract $4x$ from both sides: $5x-4x+7=4x-4x + 9$, so $x+7 = 9$. Then subtract 7 from both sides: $x=9 - 7=2$.

Step4: Find the length of LM

Substitute $x = 2$ into the expression for $LM$. Since $LM=2x + 7$, then $LM=2\times2+7$.
$LM=4 + 7=11$.

Answer:

$11$