To simplify the expression \(-5 + \frac{3}{4} (8h + 12) - 10h\), follow these steps:
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Distribute the \(\frac{3}{4}\) to both terms inside the parentheses: \[ \frac{3}{4} (8h) + \frac{3}{4} (12) = 6h + 9 \]
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Substitute this back into the expression: \[ -5 + 6h + 9 - 10h \]
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Combine the constant terms \(-5\) and \(9\): \[ -5 + 9 = 4 \]
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Combine the \(h\) terms \(6h - 10h\): \[ 6h - 10h = -4h \]
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Putting it all together: \[ 4 - 4h \]
So, the simplified expression is: \[ \boxed{4 - 4h} \]