To solve the equation \( 4(3x + 2) + 3 = 35 \), we can follow these steps:
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Start by distributing the \( 4 \) in front of the parentheses:
\[ 4 \times 3x + 4 \times 2 + 3 = 35 \]
This simplifies to:
\[ 12x + 8 + 3 = 35 \]
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Now, combine the constant terms:
\[ 12x + 11 = 35 \]
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Next, isolate the term with \( x \) by subtracting \( 11 \) from both sides:
\[ 12x = 35 - 11 \]
This simplifies to:
\[ 12x = 24 \]
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Finally, divide both sides by \( 12 \) to solve for \( x \):
\[ x = \frac{24}{12} = 2 \]
Thus, the solution is:
\[ \boxed{2} \]