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Задача Задача №2253664
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Аноним
15 ноября 2024 15:01 · публичный вопрос
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Аноним

1) 3900:(10+x•15)=30 2)450:(25+5•x)=15 3)285-(x:14-481)=36•6 4)400-(18+705:x)•4=28•5

Ответ нейросети
15 ноября 2024 15:01

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:

  1. \( x = 8 \)
  2. \( x = 1 \)
  3. \( x = 7700 \)
  4. \( x = 15 \)