Derivation of Lorentz Time Transformation

[Eipi]

Homework Statement

Derive the Lorentz Time Transformation

Relevant Equations

g (I am using g instead of gamma)=1/sqrt(1-v^2/c^2)
x'=(x-vt)/sqrt(1-v^2/c^2)

I have to derive the Lorentz time transformation given the equation for gamma and the equation for the Lorentz space transformation.
I started by using relevant equations from the Space derivation done in class (also the one that Ramamurti Shankar does). Here is a picture of what I have tried. (Yes, I am using g instead of gamma).

 

[Ibix]

You've made an arithmetic slip between the bottom of the first column and the top of the second. Correct that and it should come out right.

 

[anuttarasammyak]

On the white board you write
$$x'=\frac{x-vt}{\sqrt{1-v^2/c^2}}$$
So you can expect by relativity with changing v to -v,
$$x=\frac{x'+vt'}{\sqrt{1-v^2/c^2}}$$
It enables you to express t' by x and t.

 

[Eipi]

I spotted my algebraic mistake! Thank you so much!