To solve the equation \(0.24 (x - 10.2) = 6\), follow these steps:
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Distribute \(0.24\) on the left side: \[ 0.24x - 0.24 \cdot 10.2 = 6 \] Calculate \(0.24 \cdot 10.2\): \[ 0.24 \cdot 10.2 = 2.448 \] So the equation now looks like: \[ 0.24x - 2.448 = 6 \]
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Add \(2.448\) to both sides: \[ 0.24x = 6 + 2.448 \] Calculate \(6 + 2.448\): \[ 6 + 2.448 = 8.448 \] So now we have: \[ 0.24x = 8.448 \]
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Divide both sides by \(0.24\) to solve for \(x\): \[ x = \frac{8.448}{0.24} \] Calculate \(x\): \[ x = 35.2 \]
Therefore, the solution is: \[ \boxed{35.2} \]