M is the midpoint of LM

Question

LM=3x+5
LN=5x+40
Find MN

I've tried to work this out several times and am pretty sure I start it off by 3x+5=5(x)+40 but I keep getting a negative answer or a fraction for X and know that is not right. Can someone please help me?

Answer 1

Nope. LM cannot be the midpoint of LM.

If N is the midpoint of LM, then
LN is half of LM, so

3x+5 = 2(5x+40)
3x+5 = 10x + 80
7x = -75
that makes the lengths negative. So, we must have M is the midpoint of LN. In that case,

5x+40 = 2(3x+5)
5x+40 = 6x + 10
x = 30
So, LM=MN=95
and LN = 190

Answer 2

L is the midpoint then.
(3x+5)=(5x+40)
subtract 3x on both sides.
5=2x+40
subtract 40 on both sides.
-35=2x
divide by 2.
-17.5=x
so yes, it does come out to be negative and a decimal.