M is the midpoint of line segment LN. Find the length of LN

Step-by-step explanation:

Here is the complete question;

M is the midpoint of line segment LN. If LM= 3x + 5 and LN= 5x + 40, find the length of LN.

Since M is the midpoint of LN, hence LM + MN = LN and LM = MN

LM + LM = LN

2LM = LN *

Given;

LM= 3x + 5

LN= 5x + 40

Substitute into the eqn *

2(3x+5) = 5x+40

6x+10 = 5x+40

6x-5x = 40-10

x = 30

Get the length LN

LN= 5x + 40

LN = 5(30)+40

LN = 150+40

LN = 190

Hence the length of LN is 190

step-by-step explanation:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5