Solution
For this case we know that M is the midpointof the line LN
And we also know that:
LM= 5x+4 , MN= 12x-24
Then we can find the value of x using this equation:
LM = MN (By definition of midpoint)
Replacing we got:
5x+4= 12x-24
Solving we have:
4+24 = 12x -5x
28 = 7x
x= 28/7= 4
And solving for LN we got:
LN= LM + MN
LM= 5*4+4= 24
MN= 12*4 -24=24
Then:
LN= 24+24= 48