I have converted an audio tape to MP3 using audacity. I can play it back in the computer but if I try to play it in my regular CD player or in my car there is no sound and I get a message saying “check the CD”. 
You have probably created a “data CD” rather than a “music CD” - see this tutorial from the Audacity Manual: http://manual.audacityteam.org/o/man/burning_music_files_to_a_cd.html
WC
Once you’ve got that solved…
Note that Audio CDs are uncompressed and they are limited to about 80 minutes. (If you feed an MP3 into your CD burning software and make an audio CD, it will be automatically decompressed.)
I have converted an audio tape to MP3…
If you are making an audio CD, it’s best to avoid MP3. CDs are 44.1kHz, 16-bit, stereo, and you’ll get the best results if you create a 44.1kHz, 16-bit WAV file, and use that file to create the CD. (Audio CDs don’t have WAV files, but the underlying data is the same.)
MP3 is lossy compression, so it’s “good practice” to avoid it during audio production. (Decompressing does not un-do the “damage”.)
MP3 is better than cassette tape, and in some cases a high-quality, high-bittrate, MP3 can sound identical to the uncompressed original. But, if you want MP3 format, it’s best to compress ONCE as the LAST STEP.
Also, note that Audacity (and all “normal” audio editors) must decompress an MP3 before editing. So, if you start with an MP3 and re-save it as MP3 after editing, it has to go through a 2nd lossy-compression step. Sometimes you have no choice, but when you have a choice and you want MP3, compress once.
Are either of your CD players supposed to play MP3 data files? Some can but most can’t. As others mentioned you’ll most likely have to create an audio CD from your files that’ll play in CD players. I agree converting them to WAVs instead of MP3s would be better for an audio CD.