Question

m is the midpoint of $overline{ln}$. if $lm = 5x$ and $ln = 12x - 8$, what is $lm?
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 given expressions

Substitute $LM = 5x$ and $LN=12x - 8$ into $2LM = LN$. We get $2\times(5x)=12x - 8$.

Step3: Simplify the left - hand side

$10x=12x - 8$.

Step4: Solve for $x$

Subtract $10x$ from both sides: $0 = 12x-10x - 8$, which simplifies to $0 = 2x - 8$. Then add 8 to both sides: $8 = 2x$. Divide both sides by 2, so $x = 4$.

Step5: Find $LM$

Substitute $x = 4$ into the expression for $LM$. Since $LM = 5x$, then $LM=5\times4=20$.

Answer:

20