Given point C is on segment AB,AB= 13x-22,AC=2x+10,BC=5x-2, solve for x

Question

I need help figuring out this problem step by step because it is kind of difficult to figure out. I also need to know what to do to solve problems like these.

Answer 1

since AB includes C

from segment addition postulate : AB = AC + CB

13x -22=(2x+10)+(5x-2)

13x-7x=22+10-2

6x=30

divide both sides by 6

x=5

Answer 2

Since C is between A and B, we can deduct the following relationship:

AB = AC + CB

Let's substitute...

(13x - 22) = (2x +10) + (5x - 2)

Combine like terms and solve for x.

x = 5

Answer 3