To simplify the expression \(-34r + 3 - 56r - 6\), we will combine like terms.
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Combine the \(r\) terms: \[ -34r - 56r = -90r \]
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Combine the constant terms: \[ 3 - 6 = -3 \]
Putting it all together, we get: \[ -90r - 3 \]
Thus, the simplified expression is: \[ \boxed{-90r - 3} \]