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You are given this, right?
\(\dfrac{AB}{BC} = \dfrac{3}{4} \)

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right..

Now replace AB and BC with the lengths given in the figure.
What do you get?

|dw:1433800191984:dw|

\(\dfrac{90}{10x-20} = \dfrac{3}{4}\)
Ok?

oh okay

-20 is not the length of BC. The entire expression 10x - 20 is.
See my equation above?

Now we solve that equation.

When you have a fraction equal to a fraction, you can cross multiply.

|dw:1433800210299:dw|

so x=14?????

|dw:1433800248981:dw|

x=14 right?

I just have a hard time making the equations.

Can you help me with a few more questions?

Find the value of x.
A.
7
B.
9
C.
11
D.
12

Do you know the triangle angle bisector theorem?

I just don't know how to write an equation to solve.

That is a very cumbersome way to express this:
|dw:1433800821218:dw|

Compare the above figure to your problem.

|dw:1433801007502:dw|

Here is the fugure from your problem with the letter "y" added.

I'm not really following....

wait! So it would be 9??? I think I'm understanding.

so it isn't 9?

28x = 36(16 - x)
28x = 576 - 36x
64x = 576
x = 9

You are correct.

YAY!!! Thanks! can you help me with one more?

last one:
Find the value of each variable.
A.
a = 15, b = 5, c = 8, d = 4
B.
a = 15, b = 4, c = 8, d = 5
C.
a = 14.5, b = 5, c = 6, d = 4
D.
a = 14.5, b = 4, c = 6, d = 5

Do you understand what to do?

yes! Thank you very much for all your help!

You're welcome.

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