To solve the equation ( 9 \frac{2}{7} - (x + 2.25) = 2 \frac{5}{28} ), we will first convert the mixed numbers to improper fractions and decimals where necessary.

Convert mixed numbers to improper fractions:

( 9 \frac{2}{7} = \frac{9 \times 7 + 2}{7} = \frac{63 + 2}{7} = \frac{65}{7} )( 2 \frac{5}{28} = \frac{2 \times 28 + 5}{28} = \frac{56 + 5}{28} = \frac{61}{28} )

Thus, the equation becomes:
[
\frac{65}{7} - (x + 2.25) = \frac{61}{28}
]

Convert (2.25) to a fraction:

( 2.25 = \frac{9}{4} )

Now substitute it back into the equation:
[
\frac{65}{7} - \left(x + \frac{9}{4}\right) = \frac{61}{28}
]

Distribute:
[
\frac{65}{7} - x - \frac{9}{4} = \frac{61}{28}
]

Combine like terms:
[
\frac{65}{7} - \frac{9}{4} - x = \frac{61}{28}
]

To combine (\frac{65}{7}) and (-\frac{9}{4}), we need a common denominator:

The least common multiple of (7) and (4) is (28).

Converting:
[
\frac{65}{7} = \frac{65 \times 4}{7 \times 4} = \frac{260}{28}
]
[
\frac{9}{4} = \frac{9 \times 7}{4 \times 7} = \frac{63}{28}
]

Now the equation looks like:
[
\frac{260}{28} - x - \frac{63}{28} = \frac{61}{28}
]

Combine (\frac{260}{28}) and (-\frac{63}{28}):
[
\frac{260 - 63}{28} - x = \frac{61}{28}
]
[
\frac{197}{28} - x = \frac{61}{28}
]

Add (x) to both sides:
[
\frac{197}{28} - \frac{61}{28} = x
]

Now simplify:
[
x = \frac{197 - 61}{28} = \frac{136}{28}
]

Reduce the fraction:
[
\frac{136}{28} = \frac{34}{7}
]

Thus, the solution to the equation ( 9 \frac{2}{7} - (x + 2.25) = 2 \frac{5}{28} ) is:
[
x = \frac{34}{7}
]
or approximately (4.857) (if you prefer a decimal representation).