The problem is to evaluate the expression $(8 + \frac{28}{3}) - (\frac{1}{2} - \frac{7}{3})$.

1. Problem Description

The problem is to evaluate the expression $(8 + \frac{28}{3}) - (\frac{1}{2} - \frac{7}{3})$.

2. Solution Steps

First, we simplify the expression within the first parentheses.

$8 + \frac{28}{3} = \frac{8 \times 3}{3} + \frac{28}{3} = \frac{24}{3} + \frac{28}{3} = \frac{24 + 28}{3} = \frac{52}{3}$

Next, we simplify the expression within the second parentheses.

$\frac{1}{2} - \frac{7}{3} = \frac{1 \times 3}{2 \times 3} - \frac{7 \times 2}{3 \times 2} = \frac{3}{6} - \frac{14}{6} = \frac{3 - 14}{6} = \frac{-11}{6}$

Now, we substitute these results back into the original expression.

$(8 + \frac{28}{3}) - (\frac{1}{2} - \frac{7}{3}) = \frac{52}{3} - (\frac{-11}{6}) = \frac{52}{3} + \frac{11}{6}$

To add these fractions, we need a common denominator, which is

6. $\frac{52}{3} + \frac{11}{6} = \frac{52 \times 2}{3 \times 2} + \frac{11}{6} = \frac{104}{6} + \frac{11}{6} = \frac{104 + 11}{6} = \frac{115}{6}$

3. Final Answer

$\frac{115}{6}$