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