Answer: LM = 6 units.
Step-by-step explanation: Given that the point M is the mid-point of the line segment LN shown in the figure.
We are to find the length of LM.
From the figure, we note that
LM = 3x and MN = 2x + 2.
Since M is the mid-point of LN, so it will divide LN in two equal parts.
That is, we must have
[tex]LM=MN\\\\\Rightarrow 3x=2x+2\\\\\Rightarrow 3x-2x=2\\\\\Rightarrow x=2.[/tex]
Therefore, we get
[tex]LM=3\times2=6~\textup{units}.[/tex]
Thus, LM = 6 units.
