To solve the equation \( 9x + 16 = 6x + 1 \), follow these steps:
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Subtract \( 6x \) from both sides: \[ 9x - 6x + 16 = 1 \] which simplifies to: \[ 3x + 16 = 1 \]
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Subtract 16 from both sides: \[ 3x = 1 - 16 \] which simplifies to: \[ 3x = -15 \]
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Divide both sides by 3: \[ x = \frac{-15}{3} \] which simplifies to: \[ x = -5 \]
Thus, the solution is: \[ \boxed{-5} \]