Algebra help with Lorentz Transformation

[Luckier]

Homework Statement

Hey all, my algebra isn't as great as it used to be and I am having trouble with some of the algebra dealing with Lorentz transformation. Basically, I just need someone to do a quick step by step of how to go from x' to x (see the following).

I started with the top equation in this image (x')

and moved some things around to solve for x

Then I tried plugging in for t to put into terms of t'

This is where I am stuck, somehow I keep ending up with an extra x' and v that I cannot get rid of... By the way, the result is supposed to end up being

So I was hoping for someone to do a quick little algebra step by step so I can figure out where I made my mistake(s). This is my first time posting, I hope all the images work. If needed, here is where I obtained the images... http://galileo.phys.virginia.edu/classes/252/lorentztrans.html
Thanks in advanced for any help!

 

[vela]

Homework Statement

Hey all, my algebra isn't as great as it used to be and I am having trouble with some of the algebra dealing with Lorentz transformation. Basically, I just need someone to do a quick step by step of how to go from x' to x (see the following).

I started with the top equation in this image (x')

and moved some things around to solve for x

Then I tried plugging in for t to put into terms of t'

This is where I am stuck, somehow I keep ending up with an extra x' and v that I cannot get rid of...

What did you do after this? Did you use the second equation to substitute in for t in the first equation?

 

[Luckier]

What did you do after this? Did you use the second equation to substitute in for t in the first equation?

Hey, thanks for the reply. First I just rearranged the very first equation to get

And then I plugged in for t (into the equation above), using this equation for t:

And basically, I can't figure out the algebra. Supposedly, you should end up with

according to http://galileo.phys.virginia.edu/classes/252/lorentztrans.html

And that's it really, I just need someone to write out the steps algebraically for plugging in that t into x=vt+x'√(1-v²/c²) to get

 

[vela]

It's against the forum rules to do the problem for you. You need to show us what you did, so we can see where you're going astray. So what did you do next?