To solve the equation \(58(x + \frac{1}{2}) = 100\), we can follow these steps:
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Distribute the 58 across the parentheses: \[ 58x + 29 = 100 \]
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Subtract 29 from both sides: \[ 58x = 100 - 29 \] \[ 58x = 71 \]
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Divide both sides by 58: \[ x = \frac{71}{58} \]
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Simplify the fraction:
- \(71\) and \(58\) have no common factors, so we keep it as \(\frac{71}{58}\).
- Converting \(\frac{71}{58}\) to a mixed number: \[ 71 \div 58 = 1 \text{ R } 13 \] Therefore, \[ x = 1 \frac{13}{58} \]
Since none of the responses from the provided options seem to directly match \(\frac{71}{58}\) or its decimal equivalent, a check of the possible answers given (160 1/2, 62, 159 1/2, 63) reveals that they do not correspond to our calculated value of \(x\).
Thus, let's compute \( \frac{71}{58} \) as a decimal for clarity: \[ \frac{71}{58} \approx 1.224137931 \]
If you belong to a specific answer format aiming for mixed numbers, fractional forms, or the like, please provide clarification for proper interpretation—but per my calculation, normalizing from above gives \(x \approx 1.22\) or as approximated \(1 \frac{13}{58}\).
To summarize, please refer to the original solutions prompted earlier in hypothetical ranges; thus the direct interpretation from the input values did not yield \(x\) in predictable ranges confirmed. However, none of the choices outlined correspond accordingly to the result achieved through the algebraic resolution.