As the other Attorney stated, there is no law or requirement in Texas that requires an employer to write up an employee a number of times prior to termination. Texas is an "employment at will" state. This means that, unless there is a contract or an otherwise enforceable agreement (collective bargaining agreement), employers have the right to hire or fire an employee at anytime or for any reason, that is not unlawful, and the employer's motive will not be questioned. An employee is free to accept or terminate employment at any time. You may want to check your employee handbook for the disciplinary and termination policy. Keep in mind that most employers reserve the right to immediately terminate an employee.
Your employer is not required to follow any particular disciplinary process although if the employer has a progressive disciplinary policy and did not follow it then that usually helps you in a claim for unemployment benefits. However, that is not guaranteed. If the manager believed you were a risk to the company because you were not properly carding people then terminating you without the progressive discipline may have been appropriate.
Texas is an employment at will state. Typically, unless an employee has an employment contract, or is employed under a collective bargaining agreement through a union, the employer can modify or terminate the employment at any time with or without cause. If an employer, at any time, decides they no longer want to employ someone, for any non-discriminatory reason, that employee can legally be terminated. However, an employer generally cannot terminate an employee for prohibited discriminatory reasons (such as racial discrimination), or in retaliation for certain protected actions (such as whistle-blowing). The description of the situation, which you have provided, does not include the elements of prohibited discrimination.
Additionally, employers are not required to treat all employees the same, so long as the disparate treatment is not part of prohibited discrimination or retaliation (as described above).
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