Hello,

This code should work :

Code:

\begin{tabular}[t]{|l|ccccc|c|}
\multicolumn{7}{c}{table of basic solutions}\\\hline
&$x_{1}$&$x_{2}$&$x_{3}$&$x_{4}$&$x_{5}$&$f $\\ \hline %modified
A&4&0&-4&0&-3&4\\
B&2&0&0&2&-1&2\\
C&1&0&2&3&0&1\\
D&0&0&4&4&1&0\\
E&0&-1&5&6&0&-1\\
F&0&2&2&0&3&2\\
G&0&4&0&-4&5&4\\
H&$\frac{4}{3}$&$\frac{4}{3}$&0&0&1&$\frac{8}{3}$\\ %modified
I&2&1&-1&0&0&3\\
J&$\frac{5}{3}$&$\frac{2}{3}$&0&1&0&$\frac{7}{3}$\\ \hline %modified
\end{tabular}

I've added extra $ where needed : in each cell of the table where you use \frac{}{} or x_{}. You can't set a whole line of a table in math mode simply by enclosing it into to $. Instead, you have to enclose the content of each cell by $. I've also replaced every \x_{} by x_{} on line 3 (that may not be what you want if you did define the command \x ...).

If every cell of the table must be in math mode, you can use *array* instead of *tabular*. Every cell of an *array* is in math mode so there is no need to use the symbol $. The following code gives the table on the attached picture (note that the first column is in italic font which, again, may not be what you want).

Code:

\begin{array}[t]{|l|ccccc|c|}
\multicolumn{7}{c}{\text{table of basic solutions}}\\\hline
&x_{1}&x_{2}&x_{3}&x_{4}&x_{5}&f \\ \hline %modified
A&4&0&-4&0&-3&4\\
B&2&0&0&2&-1&2\\
C&1&0&2&3&0&1\\
D&0&0&4&4&1&0\\
E&0&-1&5&6&0&-1\\
F&0&2&2&0&3&2\\
G&0&4&0&-4&5&4\\
H&\frac{4}{3}&\frac{4}{3}&0&0&1&\frac{8}{3}\\ %modified
I&2&1&-1&0&0&3\\
J&\frac{5}{3}&\frac{2}{3}&0&1&0&\frac{7}{3}\\ \hline %modified
\end{array}