Question

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

Answer 1

Answer:

$XY=52\\\\YZ=79\\\\XY=131$

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:

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

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:

$\frac{13x}{13} =\frac{143}{13} \\\\x=11$

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