Question

m is the midpoint of ln. lm = 2x + 1. ln = 10x - 3. what is the length of ln?

Explanation:

Step1: Use mid - point property

Since M is the mid - point of LN, then $LN = 2LM$. We know that $LM=2x + 1$ and $LN = 10x-3$. So, $10x-3=2(2x + 1)$.

Step2: Solve the equation for x

Expand the right - hand side: $10x-3 = 4x+2$. Subtract $4x$ from both sides: $10x-4x-3=4x - 4x+2$, which simplifies to $6x-3 = 2$. Add 3 to both sides: $6x-3 + 3=2 + 3$, so $6x=5$. Then $x=\frac{5}{6}$.

Step3: Find the length of LN

Substitute $x = \frac{5}{6}$ into the expression for LN. $LN=10x-3=10\times\frac{5}{6}-3=\frac{50}{6}-3=\frac{50}{6}-\frac{18}{6}=\frac{50 - 18}{6}=\frac{32}{6}=\frac{16}{3}$.

Answer:

$\frac{16}{3}$