Rx7 fc won't idle
 

I've tried just about everything and read everywhere to try and fix this problem. But I've had no dice. I've set the tps sensor where it is supposed to be. The compression and spark is fine. The vacuums have been checked. I have had no luck in getting the car to run properly. The best I've gotten it to do is idle at 3000 rpm by getting it to temperature and tightening the throttle cable as much as possible. I don't know what I'm missing. Somebody. Please help me. I'm running out of ideas. I'm not the most knowledgeable, but I've done just about everything I know to troubleshoot this issue.
For spec purposes it is an s4 n/a 88 convertible.
Thank you for your time.

Have you tested the BACV? If that fails it can do wonky things. Usually a no idle condition is related to a large vacuum leak. You started that you checked this. How did you check for vacuum leaks?

First off thank you. I replaced the BAC valve with a spare one I had. But how exactly would I test it? I checked the vacuum tubes by squirting soapy water on them and replacing the ones that needed to be replaced. I also checked the vacuum diagram to make sure they where connected right.
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The Factory Service Manual has a procedure for testing it, but the quick and dirty way is take the valve off and connect one of its terminals (with a wire) to the negative pole of the battery. Then connect a separate wire to the positive pole, and (carefully and quickly) tap it on the other terminal of the BAC connector. You should hear a clicking noise. If there is no noise, the valve is stuck.

As for your high idle, no offense, but have you tried the idle screw? It's on top of the throttle body, usually there is a little rubber cap on top of it. Warm the car up. Take the cap of, turn the screw clockwise to decrease idle.