To solve the equation \(11x + 6 = 83\), follow these steps:
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Subtract 6 from both sides of the equation:
\[ 11x + 6 - 6 = 83 - 6 \]
This simplifies to:
\[ 11x = 77 \]
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Next, divide both sides by 11:
\[ x = \frac{77}{11} \]
Simplifying this gives:
\[ x = 7 \]
So, the solution is \(x = 7\).