To simplify the expression \(5a - 8c + b + 3c - 9a + 6b\), we first combine like terms.
-
Combine the \(a\) terms: \[ 5a - 9a = -4a \]
-
Combine the \(b\) terms: \[ b + 6b = 7b \]
-
Combine the \(c\) terms: \[ -8c + 3c = -5c \]
Putting it all together, we get: \[ -4a + 7b - 5c \]
Thus, the simplified expression is: \[ \boxed{-4a + 7b - 5c} \]