To solve the equation \( 0.8(10x + 13) = 3.1(0.2x + 5) \), we will start by expanding both sides.
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Expand the left side: \[ 0.8(10x + 13) = 0.8 \cdot 10x + 0.8 \cdot 13 = 8x + 10.4 \]
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Expand the right side: \[ 3.1(0.2x + 5) = 3.1 \cdot 0.2x + 3.1 \cdot 5 = 0.62x + 15.5 \]
Now the equation looks like this: \[ 8x + 10.4 = 0.62x + 15.5 \]
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Next, we'll isolate the \(x\) terms on one side and the constant terms on the other. Subtract \(0.62x\) and \(10.4\) from both sides: \[ 8x - 0.62x = 15.5 - 10.4 \]
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Simplifying both sides gives: \[ 7.38x = 5.1 \]
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Now, divide by \(7.38\) to solve for \(x\): \[ x = \frac{5.1}{7.38} \]
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Using a calculator to compute this division: \[ x \approx 0.6916 \]
Thus, the solution is: \[ \boxed{0.6916} \]