rbwinn a écrit :
You neglect the fact that if x or x' is negative in the equations
x=ct, x'=ct', then either the velocity of light has to be negative or
time has to be negative.

You're right that in the case of x=ct, when t in negative, so is x...
So what ?

The equations you gave would apply only to
positive values of x and x',

Where did you get this ? I used the equation of propagation
of light x=ct, which applies either when t or x are negative
or positive, and the LT which apply for any x,t, positive or
negative.

meaning that a photon is traveling in the
+x direction relative to the x axis.

x=ct means that light is traveling in the (Ox) (call this
+x if you want) direction and that x=0 at t=0. This equation
of movement applies as well for x,t being negative or positive.

[snip unrelated nonsense]