2007 equinox beeping when unlocking

thats normal gm programmed their alarm system that way

Press the unlock button on your vehicle's key fob to deactivate the alarm.

If you've misplaced your remote for the car, use the PATS programmed key to unlock the driver's side door.

Then, put the key in the ignition and turn the key to the "on" position. The vehicle's battery should be on, but the engine shouldn't be running.

Locate the override button on the alarm box, beneath the driver's side of the dashboard.

Press the button and hold it in until the alarm beeps one time. The LED light for the alarm should stop blinking, indicating the anti-theft system is disabled.

To reset the vehicle's alarm, put the PATS programmed key in the ignition and turn the key to the "on" position. Press the override button.

When the alarm resets, it chirps two times and the LED light begins blinking.

The best way is to remove both the battery cables from your car battery and leave them off for 12 minutes. Then put the battery cables back on and tighten them up tight. Take your key and put it into the driver door. Lock and unlock the door 3 times. This should deactivate the anti theft system. If you need further assistance troubleshooting your vehicle, then seek out a technician, such as one from YourMechanic, that can assist you with the anti theft system. Auto Repair by Top Rated Mobile Mechanics YourMechanic

Go to online store reliable they have repair manuals I am sure you will get the solution. Here's the link
https://www.reliable-store.com/products/saab-9-7x-2005-2006-2007-2008-2009-workshop-service-repair-manual

SEE THE STEPS WITH CAREFULLY AND COMMON SENSE:God bless you
Press the unlock button on your vehicle's key fob to deactivate the alarm. If you've misplaced your remote for the car, use the PATS programmed key to unlock the driver's side door. Then, put the key in the ignition and turn the key to the "on" position. The vehicle's battery should be on, but the engine shouldn't be running.

2 Locate the override button on the alarm box, beneath the driver's side of the dashboard. Press the button and hold it in until the alarm beeps one time. The LED light for the alarm should stop blinking, indicating the anti-theft system is disabled.

3 To reset the vehicle's alarm, put the PATS programmed key in the ignition and turn the key to the "on" position. Press the override button. When the alarm resets, it chirps two times and the LED light begins blinking.

Try using your spare key to lock and then unlock the car. This may reset the anti-theft system. This applies to the alarm as well.

TURN ON IGNITION SWITCH TO ON POSITION.ENGINE OFF.REPEATEDLY PRESS VECHICLE INFORMATION BUTTON UNTIL PRESS TO RELEARN REMOTE KEY IS DISPLAYED.PRESS SET RESET BUTTON UNTIL REMOTE KEY LEARNING ACTIVE IS DISPLAYED. IF THAT PROCEDURE DONT WORK.INSERT MASTER KEY INTO IGNITION SWITCH.NOW SWITCH IGNITION ON SWITCH IGNITION OFF.REMOVE MASTER KEY.WITHIN 10 SECONDS INSERT NEW KEY.SWITCH IGNITION ON.ENSURE SYSTEM WARNING LAMP SWITCHES OFF.NEW KEY NOW PROGRAMMED.IF YOU STILL HAVING PROBLEM RESETING THEFT SECURITY SYSTEM THE DEALERSHIP HAS TO FIX.REPROGRAM IT.

Put the key in the driver door lock (or the trunk lock if you don't trust the driver's door- quite often on a vehicle of this age the wires break in the door and it won't electrically de-activate the alarm due to the broken wires)
Disconnect the battery.
Turn the key to the unlock position (toward the front of the car if using the driver or passenger doors) and release it- it will go back to centered, but will retain slack in the forward direction
Then reconnect the battery. You may get one beep out of the alarm horn. If it beeps continually, turn the key to unlock again.
As long as the alarm is de-activated it will not prevent the car from starting. If you are still having a problem it is not alarm related.

Good luck and keep me posted, be glad to help