To solve the equation \( 11x + 29 = 82 \), follow these steps:
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Subtract 29 from both sides: \[ 11x = 82 - 29 \] \[ 11x = 53 \]
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Divide both sides by 11: \[ x = \frac{53}{11} \] \[ x \approx 4.8181 \]
Since the options given are integers (5, 6, 11, 10), the closest integer value for \( x \) is \( 5 \).
Therefore, the best estimate of \( x \) is 5.