Let's simplify the expression \(3(4x + 1) - 1 - x\) step by step.
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Distribute the \(3\) to both terms inside the parentheses: \[ 3(4x) + 3(1) = 12x + 3 \]
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Now, rewrite the expression: \[ 12x + 3 - 1 - x \]
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Combine the constant terms \(3\) and \(-1\): \[ 12x + 2 - x \]
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Now, combine the like terms \(12x\) and \(-x\): \[ (12x - x) + 2 = 11x + 2 \]
So, the completely simplified expression is: \[ \boxed{11x + 2} \]
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