So someone help me explain how they found the solution to this Example 2?

Step-by-step explanation:

The line segment would like something like so:

X--------------------------Y---------------------------Z

The segment addition postulate says that x------y + y-------z = x-------y--------z

You are given the following measures for each:

            5x-3                         8x-9

X--------------------------Y---------------------------Z

|______________131______________|

You now need to substitute this in for the postulate:

Simplify the equation to solve for the value of x. Remove the parentheses:

Combine like terms to simplify the equation (make sure to keep the symbol of a term the same when combining. For example, since the negative symbol is in front of the three, it will be -3):

Use inverse operations. Add 12 to both sides:

Use inverse operations to isolate the variable. Divide both sides by 13:

Now that we know the value of x, we can insert its value into each given length to simplify:

--------------------

------------------

To make sure the values are true, insert them into the postulate:

Since the equation is true:

              52                            79

X--------------------------Y---------------------------Z

|______________131______________|

:Done

sometimes it can be so they can fit in with a certain group, and others are just like that because of their personality.