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Reference Frames - Proving that Two Events are not Simultaneous in a System

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Consider two events in the S-system that occur at different points (x, y, z) and (x2, y2, z2) but at the same time t0. Show that these two events are not simultaneous in the S' system but are separated by a time interval -V*gamm*change in x/c^2 (see attachment for equation written out in symbols).

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Solution Summary

The solution proves that two events are not simultaneous in a system.

Solution Preview

From the statement of the question it appear that S' moves along the X-axis with velocity V.
The Lorentz transformation in this case is
...

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