To simplify the expression \( 14 - 5\left(\frac{4}{5}\right) + 7 \), follow these steps:
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Calculate \( 5\left(\frac{4}{5}\right) \): \[ 5 \cdot \frac{4}{5} = 4 \]
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Substitute this back into the expression: \[ 14 - 4 + 7 \]
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Now perform the operations from left to right: \[ 14 - 4 = 10 \] \[ 10 + 7 = 17 \]
Thus, the simplified result is: \[ \boxed{17} \]