To evaluate the expression \( \frac{1}{2} b + 58 \times 2 \) when \( b = 114 \), we can follow these steps:
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Substitute \( b = 114 \) into the expression: \[ \frac{1}{2} (114) + 58 \times 2 \]
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Calculate \( \frac{1}{2} (114) \): \[ \frac{1}{2} (114) = 57 \]
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Calculate \( 58 \times 2 \): \[ 58 \times 2 = 116 \]
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Now, combine the results: \[ 57 + 116 = 173 \]
Thus, the value of the expression is \( \boxed{173} \).