Question

m is the midpoint of $overline{ln}$. if $lm = 6x + 10$ and $mn = 9x - 8$, 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 \(LM = MN\). So we set up the equation \(6x + 10=9x - 8\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(10 = 9x-6x - 8\), which simplifies to \(10 = 3x - 8\). Then add 8 to both sides: \(10 + 8=3x\), so \(18 = 3x\). Divide both sides by 3, we get \(x = 6\).

Step3: Find \(LM\)

Substitute \(x = 6\) into the expression for \(LM\). \(LM=6x + 10\), so \(LM=6\times6 + 10=36 + 10=46\).

Answer:

46