How do I know which Lorentz trasnform equations to use?

[Kushwoho44]

Homework Statement

1. Two events occur at the same place in a certain inertial frame and are separated
by a time interval of 4 s. What is the spatial separation between these two events
in an inertial frame in which the events are separated by a time interval of 6 s?

Homework Equations

There are two equations here that relate time in different inertial frames:

t' = γ (t - vx/c^2)

and

t= γ (t' + x'/c^2)

The Attempt at a Solution

I want to obtain the value of γ from one of these equations but of course, they will give me different answers, how do I know which one to use?

Thanks for your time.

 

[Chestermiller]

Have you learned about the following equation, which is derived directly from the Lorentz Transformation:
$$(Δx)^2-(cΔt)^2=(Δx')^2-(cΔt')^2$$