Let's solve the equation step by step.

You have written the equation twice, but I'll interpret it as a single equation. It seems you wanted to solve:

\[
\frac{9}{2} - \left(\frac{2}{3} - \left(x + \frac{7}{4}\right)\right) = -\frac{5}{4}
\]

Now, let's break it down:

1. First, simplify the left side of the equation:

\[
\frac{9}{2} - \left(\frac{2}{3} - x - \frac{7}{4}\right)
\]

2. Combine the terms inside the parentheses:

- To do this, we'll first find a common denominator for \( \frac{2}{3} \) and \( \frac{7}{4} \):
- The least common multiple of 3 and 4 is 12.
- Convert \( \frac{2}{3} \) and \( \frac{7}{4} \) to have a denominator of 12:

\[
\frac{2}{3} = \frac{8}{12}, \quad \frac{7}{4} = \frac{21}{12}
\]

So we have:

\[
\frac{2}{3} - \frac{7}{4} = \frac{8}{12} - \frac{21}{12} = -\frac{13}{12}
\]

3. Now substitute this back into the equation:

\[
\frac{9}{2} - \left(-\frac{13}{12} - x\right) = -\frac{5}{4}
\]

4. This simplifies to:

\[
\frac{9}{2} + \frac{13}{12} + x = -\frac{5}{4}
\]

5. Find a common denominator to combine \( \frac{9}{2} \) and \( \frac{13}{12} \):
- The least common multiple of 2 and 12 is 12.

\[
\frac{9}{2} = \frac{54}{12}
\]

So the equation becomes:

\[
\frac{54}{12} + \frac{13}{12} + x = -\frac{5}{4}
\]

6. Combine the fractional terms:

\[
\frac{67}{12} + x = -\frac{5}{4}
\]

7. Convert \( -\frac{5}{4} \) to have a denominator of 12:

\[
-\frac{5}{4} = -\frac{15}{12}
\]

8. Now the equation is:

\[
\frac{67}{12} + x = -\frac{15}{12}
\]

9. Solve for \( x \):

\[
x = -\frac{15}{12} - \frac{67}{12}
\]
\[
x = -\frac{82}{12}
\]

10. Simplifying gives:

\[
x = -\frac{41}{6}
\]

So, the solution to your equation is:

\[
\boxed{-\frac{41}{6}}
\]