Let's solve each equation step by step:
1) \( 3900:(10+x\cdot15)=30 \)
This can be rewritten as:
\[ \frac{3900}{10 + x \cdot 15} = 30 \]
Cross multiplying gives:
\[ 3900 = 30(10 + 15x) \]
Expanding the right side:
\[ 3900 = 300 + 450x \]
Now, isolate \( x \):
\[ 3900 - 300 = 450x \] \[ 3600 = 450x \] \[ x = \frac{3600}{450} = 8 \]
2) \( 450:(25+5\cdot x)=15 \)
Rewriting it gives:
\[ \frac{450}{25 + 5x} = 15 \]
Cross multiplying leads to:
\[ 450 = 15(25 + 5x) \]
Expanding gives:
\[ 450 = 375 + 75x \]
Now simplify to find \( x \):
\[ 450 - 375 = 75x \] \[ 75 = 75x \] \[ x = 1 \]
3) \( 285 - (x:14 - 481) = 36 \cdot 6 \)
First, we calculate \( 36 \cdot 6 = 216 \):
Rewriting gives:
\[ 285 - \left(\frac{x}{14} - 481\right) = 216 \]
Rearranging gives:
\[ 285 - 216 = \frac{x}{14} - 481 \] \[ 69 = \frac{x}{14} - 481 \]
Add 481 to both sides:
\[ 69 + 481 = \frac{x}{14} \] \[ 550 = \frac{x}{14} \]
Multiplying both sides by 14 gives:
\[ x = 550 \cdot 14 = 7700 \]
4) \( 400 - (18 + 705:x) \cdot 4 = 28 \cdot 5 \)
Calculating \( 28 \cdot 5 = 140 \):
Rewriting gives:
\[ 400 - (18 + \frac{705}{x}) \cdot 4 = 140 \]
Rearranging gives:
\[ (18 + \frac{705}{x}) \cdot 4 = 400 - 140 \] \[ (18 + \frac{705}{x}) \cdot 4 = 260 \]
Dividing both sides by 4 gives:
\[ 18 + \frac{705}{x} = 65 \]
Subtracting 18 from both sides gives:
\[ \frac{705}{x} = 65 - 18 \] \[ \frac{705}{x} = 47 \]
Cross-multiplying gives:
\[ 705 = 47x \]
Finally, solving for \( x \):
\[ x = \frac{705}{47} = 15 \]
Summary of solutions:
- \( x = 8 \)
- \( x = 1 \)
- \( x = 7700 \)
- \( x = 15 \)