Question 1044963
segment addition postulate states:


In geometry, the segment addition postulate states that, given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.


change the names and it becomes:


In geometry, the segment addition postulate states that given two points M and P, a third point N lies on the line segment MP if and only if the distances between the points satisfy the equation MN + NP = MP


your overall segment is mn
n is between m and p
you are given that:
mn = 3x + 2
np = 18
mp = 5x


the addition postulates says that mn + np = mp


replace mp with 5x and mn with 3x + 2 and np with 18 and you get:


3x + 2 + 18 = 5x


combine like terms to get:


3x + 20 = 5x


subtract 3x from both sides of this equation to get:


20 = 5x - 2x


combine like terms to get:


20 = 2x


solve for x to get:


x = 10


replace x with 5 and you get:


mn = 3x + 2 = 32
np = 18
mp = 5x = 50


mn + np = mp becomes 32 + 18 = 40 which becomes 50 = 50


your solution is that mn = 32