Is a verbal agreement binding in the court room in Texas?

Generally speaking, verbal agreements are enforceable in Texas. Obviously, verbal agreements are more difficult to prove, but nonetheless they are enforceable. There are certain transactions that do require a written agreement. For more on the types of transactions that require a written agreement you can read the statute itself (known as the "Statute of Frauds"):

http://law.justia.com/texas/codes/bc/003.00.000026.00.html

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DISCLAIMER—This answer is for informational purposes only and discusses general legal principles, trends, and considerations and is not intended as specific legal advice regarding your question. This answer does not establish an attorney client relationship. For legal advice, you should retain legal counsel regarding your specific circumstances.