Question

point m is on line segment $overline{ln}$. given $ln = 4x$, $mn = x$, and $lm = 3$, determine the numerical length of $overline{ln}$. answer attempt 1 out of 2 $ln=$

Explanation:

Step1: Use segment - addition postulate

Since point M is on line - segment $\overline{LN}$, we know that $LN=LM + MN$.

Step2: Substitute given expressions

We are given that $LN = 4x$, $MN=x$, and $LM = 3$. Substituting into $LN=LM + MN$, we get $4x=3 + x$.

Step3: Solve for x

Subtract x from both sides of the equation $4x=3 + x$. We have $4x−x=3$, which simplifies to $3x = 3$. Then divide both sides by 3: $x=\frac{3}{3}=1$.

Step4: Find the length of LN

Since $LN = 4x$ and $x = 1$, then $LN=4\times1 = 4$.

Answer:

4