To simplify the expression \(-5 + \frac{3}{4}(8h + 13) - 10h\), follow these steps:
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Distribute \(\frac{3}{4}\) to both terms inside the parentheses: \[ \frac{3}{4} \cdot 8h + \frac{3}{4} \cdot 13 = 6h + \frac{39}{4} \]
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Substitute this back into the expression: \[ -5 + 6h + \frac{39}{4} - 10h \]
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Combine the like terms. First, simplify the \(h\) terms: \[ 6h - 10h = -4h \]
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Now, combine the constant terms \(-5\) and \(\frac{39}{4}\). To do this, convert \(-5\) into a fraction with a denominator of 4: \[ -5 = -\frac{20}{4} \]
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Now combine the constant terms: \[ -\frac{20}{4} + \frac{39}{4} = \frac{19}{4} \]
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Put it all together: \[ -4h + \frac{19}{4} \]
The simplified expression is: \[ -4h + \frac{19}{4} \]
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