M is the midpoint of LM
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?
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
To find MN, we need to consider that M is the midpoint of LM. This means that the lengths of LM and MN are equal.
We are given that LM = 3x + 5 and LN = 5x + 40.
To find MN, we can start by setting LM equal to LN:
3x + 5 = 5x + 40
Now, let's solve this equation to find the value of x:
3x - 5x = 40 - 5
-2x = 35
x = 35 / -2
x = -17.5
Now that we have x, we can substitute it back into either LM or LN to find the lengths.
Let's substitute it into LM:
LM = 3x + 5
LM = 3(-17.5) + 5
LM = -52.5 + 5
LM = -47.5
Since M is the midpoint, we know that the lengths of LM and MN are equal. Therefore, MN is also equal to -47.5.
So, MN = -47.5.
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.