The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC
if and only if the distances between the points meet the requirements of the equation AB + BC = AC.
The picture can look roughly like this:
We can see that "R" is in-between "A" and "X".
From the postulate, we can write:
AR + RX = AX
Now,
Given
AR = 5x - 15
RX = 3x + 1
AX = 58,
We put it into the equation and find x first. Shown below:
[tex]\begin{gathered} AR+RX=AX \\ (5x-15)+(3x+1)=58 \\ 5x+3x-15+1=58 \\ 8x-14=58 \\ 8x=58+14 \\ 8x=72 \\ x=\frac{72}{8} \\ x=9 \end{gathered}[/tex]Since, we got x, we can easily find AR and RX. Shown below:
AR = 5x - 15
AR = 5(9) - 15
AR = 45 - 15
AR = 30and
RX = 3x + 1
RX = 3(9) + 1
RX = 27 + 1
RX = 28
