To simplify the expression \( 9g - 7h - 6g + 2h \), we can combine like terms.
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Combine the terms with \(g\): \[ 9g - 6g = 3g \]
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Combine the terms with \(h\): \[ -7h + 2h = -5h \]
Putting it all together, we get: \[ 3g - 5h \]
Thus, the simplified expression is \( 3g - 5h \).