There is an easy way to answer the example 2.
You have the segment that is called RT and it is divided by two segments RS and ST. So the length of RT correspond to the length of RS plus the length of ST. This correspond to the Segment Addition Postulate (informally speaking).
Now take the values of the lengths.
|RT| = 5x -12
|RS| = x +2
|ST| = 3x - 8
By the Segment Addition Postulate we can stablich the next equation
(x + 2) + (3x-8) = 5x -12
We need to know the value of x
So, first simplify the left side of the equation, that means that we need add the x's and the numbers. So, we have
4x - 6 = 5x -12
Now, we need to left the x's alone in some side (in the way to obtain a positive x), so, add -4x in both sides
-6 = x -12
finally if we add +12 in both sides, we have
6 = x. This is the answer