Question

m is the midpoint of $overline{ln}$. if $lm = 8x - 7$ and $ln = 12x - 1$, what is $ln?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since $M$ is the mid - point of $\overline{LN}$, then $LM=\frac{1}{2}LN$. So, $2LM = LN$.

Step2: Substitute the given expressions

Substitute $LM = 8x−7$ and $LN = 12x−1$ into $2LM = LN$. We get $2(8x - 7)=12x - 1$.

Step3: Expand the left - hand side

Expand $2(8x - 7)$ to get $16x-14$. So the equation becomes $16x-14 = 12x - 1$.

Step4: Solve for $x$

Subtract $12x$ from both sides: $16x-12x-14=12x - 12x - 1$, which simplifies to $4x-14=-1$. Then add 14 to both sides: $4x-14 + 14=-1 + 14$, giving $4x = 13$. Divide both sides by 4: $x=\frac{13}{4}$.

Step5: Find the value of $LN$

Substitute $x = \frac{13}{4}$ into the expression for $LN$: $LN=12x - 1=12\times\frac{13}{4}-1$. First, $12\times\frac{13}{4}=3\times13 = 39$. Then $LN=39 - 1=38$.

Answer:

38