Question

question point m is on line segment ln. given mn = 3x, ln = 4x + 9, and lm = 2x + 7, determine the numerical length of lm. answer attempt 1 out of 2 lm=

Explanation:

Step1: Use segment - addition postulate

Since $LM + MN=LN$, substitute the given expressions: $(2x + 7)+3x=4x + 9$.

Step2: Combine like - terms

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

Step3: Solve for x

Subtract $4x$ from both sides: $5x-4x+7=4x-4x + 9$, getting $x+7 = 9$. 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