86,4:(35,5-7x)=16

To solve the equation \( 86.4 : (35.5 - 7x) = 16 \), we can begin by simplifying and isolating \( x \).

1. Rewrite the expression using multiplication for clarity: \[ \frac{86.4}{35.5 - 7x} = 16 \]

2. To eliminate the fraction, multiply both sides by \( 35.5 - 7x \): \[ 86.4 = 16 \times (35.5 - 7x) \]

3. Distributing on the right side: \[ 86.4 = 568 - 112x \]

4. Now, isolate \( x \) by moving \( 112x \) to the left side and \( 86.4 \) to the right: \[ 112x = 568 - 86.4 \]

5. Calculate \( 568 - 86.4 \): \[ 568 - 86.4 = 481.6 \] So, we have: \[ 112x = 481.6 \]

6. Divide both sides by 112 to solve for \( x \): \[ x = \frac{481.6}{112} \]

7. Calculate the division: \[ x = 4.3 \]

Thus, the solution is: \[ x = 4.3 \]