Make sure that you installed the correct client (64 bit on 64 bit Linux, and 32 bit on 32 bit Linux).
Make ts3client_runscript.sh executable if it isn't already (chmod +x ts3client_runscript.sh)
run the script.
If it doesn't work for some reason check or post the script and try the following instead from within the client root directory
Code:
export LD_LIBRARY_PATH=. && ./ts3client_linux_amd64
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