HTC One X SIM Card Tray Replacement

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Before proceeding to fix the Sim Card tray, make sure the issue regarding the sim card detection isn't due to a faulty sim card.

Insert a safety pin or other small object in the small opening next to the SIM card slot to remove the SIM card.
The Sim Card Slot is located at the top of the rear panel.

Cut a piece of tape/ paper approximately the size of your Sim Card and secure it to the back side of the Sim. Be sure to trim any excess.
It's important that you place the tape on the back side of the Sim Card as it will block the communication with the device if placed on the front side
Slowly slide the Sim Card tray back into the device. It should be a smooth transition, don't force the tray in.
If the tray is still loose you can keep adding tape/paper until it's no longer loose.