Answer:
![ML=27\\LN=27\\MN=54](https://tex.z-dn.net/?f=ML%3D27%5C%5CLN%3D27%5C%5CMN%3D54)
Step-by-step explanation:
Since L is the midpoint of MN, by the definition of midpoint:
![ML=LN](https://tex.z-dn.net/?f=ML%3DLN)
We can picture the following segment:
M----------L----------N
We know that
and
. Since the two segments are equivalent, we can set them equal to each other:
![2x+7=3x-3](https://tex.z-dn.net/?f=2x%2B7%3D3x-3)
Now, let's solve for x. Subtract -7 from both sides:
![2x=3x-10](https://tex.z-dn.net/?f=2x%3D3x-10)
Subtract 3x from both sides:
![-x=-10](https://tex.z-dn.net/?f=-x%3D-10)
Divide both sides by -1:
![x=10](https://tex.z-dn.net/?f=x%3D10)
So, the value of x is 10.
With this, we can find the remaining lengths.
We know that ML is
.
Substitute 10 for x. So, the length of ML is:
![ML=2(10)+7=20+7=27](https://tex.z-dn.net/?f=ML%3D2%2810%29%2B7%3D20%2B7%3D27)
We know that LN is
. So, the length of LN is:
![LN=3(10)-3=30-3=27](https://tex.z-dn.net/?f=LN%3D3%2810%29-3%3D30-3%3D27)
Finally, MN will be the combined lengths of ML and LN. So:
![MN=ML+LN=27+27=54](https://tex.z-dn.net/?f=MN%3DML%2BLN%3D27%2B27%3D54)
And we're done!