Question

m is the mid - point of ln. if lm = x + 3 and ln = 6x - 6, what is lm? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Recall mid - point property

Since M is the mid - point of $\overline{LN}$, we know that $LM=\frac{1}{2}LN$.
So, $x + 3=\frac{1}{2}(6x - 6)$.

Step2: Solve the equation for x

Multiply both sides of the equation by 2 to get rid of the fraction: $2(x + 3)=6x - 6$.
Expand the left - hand side: $2x+6 = 6x - 6$.
Subtract $2x$ from both sides: $6=6x - 2x-6$.
Simplify to get $6 = 4x-6$.
Add 6 to both sides: $6 + 6=4x$, so $12 = 4x$.
Divide both sides by 4: $x = 3$.

Step3: Find the value of LM

Substitute $x = 3$ into the expression for $LM$. Since $LM=x + 3$, then $LM=3 + 3=6$.

Answer:

6