Question

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

Answer 1

`XY=52\\\\YZ=79\\\\XY=131`

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:

`XY=5x-3\\\\YZ=8x-9\\\\XZ=131\\\\XY+YZ=XZ\\\\(5x-3)+(8x-9)=131`

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

`5x-3+8x-9=131`

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):

`5x+8x-3-9=131\\\\13x-12=131`

Use inverse operations. Add 12 to both sides:

`13x-12+12=131+12\\\\13x=143`

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

`(13x)/(13) =(143)/(13) \\\\x=11`

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

`XY=5x-3\\\\XY=5(11)-3\\\\XY=55-3\\\\XY=52`

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

`YZ=8x-9\\\\YZ=8(11)-9\\\\YZ=88-9\\\\YZ=79`

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

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

`52+79=131\\\\131=131`

Since the equation is true:

52 79

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

|______________131______________|

:Done