Question

m is the mid - point of $overline{ln}$. if $mn = 7x + 4$ and $ln = 15x - 1$, 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 $LN = 2MN$. Given $MN=7x + 4$ and $LN = 15x-1$, we have the equation $15x-1=2(7x + 4)$.

Step2: Expand the right - hand side

Expand $2(7x + 4)$ using the distributive property. $2(7x + 4)=14x+8$. So the equation becomes $15x-1 = 14x + 8$.

Step3: Solve for $x$

Subtract $14x$ from both sides of the equation: $15x-14x-1=14x-14x + 8$, which simplifies to $x-1 = 8$. Then add 1 to both sides: $x=8 + 1=9$.

Step4: Find the value of $LN$

Substitute $x = 9$ into the expression for $LN$. $LN=15x-1=15\times9-1=135-1 = 134$.

Answer:

$134$