To simplify the expression \( 5a - 8c + b + 3c - 9a + 6b \), we can combine like terms.
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Combine the \( a \) terms: \[ 5a - 9a = -4a \]
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Combine the \( b \) terms: \[ b + 6b = 7b \]
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Combine the \( c \) terms: \[ -8c + 3c = -5c \]
Now, putting it all together, we have: \[ -4a + 7b - 5c \]
Thus, the simplified expression is: \[ -4a + 7b - 5c \]