To simplify the expression 9/2 - [ 2/3 - ( x + 7/4 ) ] - 5/4, we can start by simplifying the innermost parentheses first.

Inside the parentheses, we have ( x + 7/4 ). To simplify this further, we can combine the x term and the 7/4 term by finding a common denominator.

The common denominator for 1 and 4 is 4, so we can rewrite the expression as:

(4x/4 + 7/4)

Combining the terms, we get:

(4x + 7)/4

Now, let's substitute this simplified expression back into the original equation:

9/2 - [ 2/3 - (4x + 7)/4 ] - 5/4

Next, let's simplify the expression inside the brackets:

2/3 - (4x + 7)/4

To combine these fractions, we need a common denominator. The common denominator for 3 and 4 is 12, so we can rewrite the expression as:

(8/12 - (4x + 7)/12)

Combining the terms, we get:

(8 - (4x + 7))/12

Now, let's substitute this simplified expression back into the original equation:

9/2 - (8 - (4x + 7))/12 - 5/4

Next, let's simplify the expression inside the parentheses:

(8 - (4x + 7))

To simplify further, we can distribute the negative sign:

8 - 4x - 7

Combining like terms, we get:

(1 - 4x)

Now, let's substitute this simplified expression back into the original equation:

9/2 - (1 - 4x)/12 - 5/4

Next, let's simplify the expression (1 - 4x)/12:

(1 - 4x)/12

Finally, let's substitute this simplified expression back into the original equation:

9/2 - (1 - 4x)/12 - 5/4

Now, we can combine the fractions by finding a common denominator. The common denominator for 2, 12, and 4 is 12, so we can rewrite the equation as:

(54/12 - (1 - 4x)/12 - 15/12)

Combining the terms, we get:

(54 - (1 - 4x) - 15)/12

Now, let's simplify the expression inside the parentheses:

(54 - (1 - 4x))

To simplify further, we can distribute the negative sign:

54 - 1 + 4x - 15

Combining like terms, we get:

(38 + 4x)

Now, let's substitute this simplified expression back into the original equation:

(38 + 4x)/12

Finally, we have:

(38 + 4x)/12

Therefore, the simplified expression is (38 + 4x)/12.