To simplify the expression \( 5(0.1x - 0.2) + 10x \):
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Distribute the 5: \[ 5 \cdot 0.1x - 5 \cdot 0.2 = 0.5x - 1 \]
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Now combine this with \( 10x \): \[ 0.5x - 1 + 10x \]
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Combine the \( x \) terms: \[ 0.5x + 10x = 10.5x \]
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So the final simplified expression is: \[ 10.5x - 1 \]
Therefore, the simplified expression is \( 10.5x - 1 \).