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Solve for x

in the equation 102.5(x−11.92)=71.6
. Round your answer to 3 decimal places.(1 point)
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1 answer

To solve the equation \( 102.5(x - 11.92) = 71.6 \), we can follow these steps:

  1. Distribute the 102.5: \[ 102.5x - 102.5 \times 11.92 = 71.6 \]

    Calculating \( 102.5 \times 11.92 \): \[ 102.5 \times 11.92 = 1223.4 \] Thus, the equation simplifies to: \[ 102.5x - 1223.4 = 71.6 \]

  2. Add 1223.4 to both sides: \[ 102.5x = 71.6 + 1223.4 \] \[ 102.5x = 1295 \]

  3. Divide by 102.5 to isolate \( x \): \[ x = \frac{1295}{102.5} \]

  4. Calculating the division: \[ x = 12.63414634 \ldots \]

  5. Rounding to 3 decimal places: \[ x \approx 12.634 \]

Therefore, the final answer is: \[ \boxed{12.634} \]