To simplify the expression \(7x - 3 + 2x + 6\), we can combine like terms step by step.
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Combine the \(x\) terms: \[ 7x + 2x = 9x \]
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Combine the constant terms: \[ -3 + 6 = 3 \]
Now, put it all together: \[ 9x + 3 \]
Thus, the simplified expression is \(9x + 3\).
So the correct answer is C. \(9x + 3\).