To solve the equation \(102.5 (x - 11.92) = 71.6\), we can follow these steps:
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Distribute \(102.5\) on the left side: \[ 102.5x - 102.5 \cdot 11.92 = 71.6 \]
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Calculate \(102.5 \cdot 11.92\): \[ 102.5 \cdot 11.92 = 1224.4 \]
So, the equation becomes: \[ 102.5x - 1224.4 = 71.6 \]
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Add \(1224.4\) to both sides: \[ 102.5x = 71.6 + 1224.4 \] \[ 102.5x = 1296 \]
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Divide both sides by \(102.5\): \[ x = \frac{1296}{102.5} \]
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Calculate the division: \[ x \approx 12.650244 \]
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Round to 3 decimal places: \[ x \approx 12.650 \]
Thus, the solution for \(x\) is approximately \( \boxed{12.650} \).
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