Let's break down each equation step-by-step one by one.

### Equation 1:
\[
\frac{7}{8} : x - \frac{5}{4} = 3 - \frac{1}{27/8}
\]

First, we need to simplify \(\frac{1}{27/8}\):
\[
\frac{1}{27/8} = \frac{8}{27}
\]

Now the equation becomes:
\[
\frac{7}{8} : x - \frac{5}{4} = 3 - \frac{8}{27}
\]
For \(3 - \frac{8}{27}\), we convert 3 to a fraction with a common denominator of 27:
\[
3 = \frac{81}{27}
\]
Thus:
\[
3 - \frac{8}{27} = \frac{81}{27} - \frac{8}{27} = \frac{73}{27}
\]

The equation now becomes:
\[
\frac{7}{8} : x - \frac{5}{4} = \frac{73}{27}
\]

Next, let's rewrite \( \frac{7}{8} : x \) as \( \frac{7}{8x} \) (assuming “:” means division) and substitute to solve for \(x\).

\[
\frac{7}{8x} - \frac{5}{4} = \frac{73}{27}
\]

Now, rearranging gives:
\[
\frac{7}{8x} = \frac{73}{27} + \frac{5}{4}
\]
Finding a common denominator (which can be 108), we find:

- \(\frac{73}{27} = \frac{292}{108}\)
- \(\frac{5}{4} = \frac{135}{108}\)

Adding these together:
\[
\frac{292 + 135}{108} = \frac{427}{108}
\]
So:
\[
\frac{7}{8x} = \frac{427}{108}
\]
Cross-multiplying gives:
\[
7 \cdot 108 = 427 \cdot 8x
\]
Calculating yields:
\[
756 = 3416x \Rightarrow x = \frac{756}{3416} \Rightarrow x = \frac{189}{854}
\]

### Equation 2:
\[
1.5x + \frac{1}{2} \cdot \frac{1}{3} = \frac{3}{4}
\]
Calculating:
\[
\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}
\]
Thus:
\[
1.5x + \frac{1}{6} = \frac{3}{4}
\]
Subtracting \(\frac{1}{6}\) (common denominator is 12):
\[
\frac{3}{4} = \frac{9}{12}, \quad \frac{1}{6} = \frac{2}{12}
\]
So:
\[
1.5x = \frac{9}{12} - \frac{2}{12} = \frac{7}{12}
\]
Now, \(1.5 = \frac{3}{2}\), thus:
\[
\frac{3}{2} x = \frac{7}{12}
\]
Cross-multiplying yields:
\[
3x = \frac{7 \cdot 2}{12} \Rightarrow 3x = \frac{14}{12} = \frac{7}{6} \Rightarrow x = \frac{7}{18}
\]

### Equation 3:
\[
\frac{3}{2} \cdot \frac{4}{555} - 2x = \frac{2}{3}
\]
Calculating:
\[
\frac{3 \cdot 4}{2 \cdot 555} = \frac{12}{1110}
\]
Thus:
\[
\frac{12}{1110} - 2x = \frac{2}{3}
\]
We find a common denominator (3330):
\[
\frac{12}{1110} = \frac{36}{3330}, \quad \frac{2}{3} = \frac{2200}{3330}
\]
Subtracting gives:
\[
-2x = \frac{2200 - 36}{3330} = \frac{2164}{3330}
\]
\[
x = -\frac{1082}{3330}
\]

### Equation 4:
\[
49.8 - x : 2.4 = 29.8
\]
Assuming “:” indicates division, we write:
\[
49.8 - \frac{x}{2.4} = 29.8
\]
Rearranging gives:
\[
49.8 - 29.8 = \frac{x}{2.4} \Rightarrow 20 = \frac{x}{2.4} \Rightarrow x = 20 \cdot 2.4 = 48
\]

### Summary
1. First Equation: \( x = \frac{189}{854} \)
2. Second Equation: \( x = \frac{7}{18} \)
3. Third Equation: \( x = -\frac{1082}{3330} \)
4. Fourth Equation: \( x = 48 \)

Please let me know if you need further assistance!