M is the midpoint of LN. LM=2x+7; LN=3x+20. Find the value of LN

In this problem LN would be equal to 38.

In order to find this, we need to first note that LM will be half of LN (since M is the midpoint). As a result, we can multiply LM by 2 and set it equal to LN.

2LM = LN

2(2x + 7) = 3x + 20

4x + 14 = 3x + 20

x + 14 = 20

x = 6

Now that we have the value of x as 6, we can plug into LN to get it's value.

LN = 3x + 20

LN = 3(6) + 20

LN = 38