Worked example: A rocket passes Earth at v = 0.6c. An event occurs on the rocket at x′ = 0, t′ = 10 s (rocket frame). When and where does Earth say it happened? Step 1: Compute γ = 1/√(1 − 0.36) = 1/√0.64 = 1/0.8 = 1.25. Step 2: Invert the transformations: x = γ(x′ + vt′), t = γ(t′ + vx′/c²). Step 3: x = 1.25 × (0 + 0.6c × 10 s) = 1.25 × 6 light-seconds = 7.5 light-seconds ≈ 2.25×10⁹ m. Step 4: t = 1.25 × (10 + 0) = 12.5 s. Conclusion: Earth records the event at t = 12.5 s (not 10 s — time dilation) and 7.5 light-seconds away (the rocket has moved on). Note t ≠ t′: simultaneity and duration are frame-dependent.