To identify which of the given expressions has a linear term with a coefficient of \(-1\), we need to look for the term that is of the form \(bx\) where \(b = -1\).
Let's analyze each expression:
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\(3x^2 - x - 4\): The coefficient of the linear term \(-x\) is \(-1\).
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\(2x^2 + 6x - 12\): The coefficient of the linear term \(6x\) is \(6\).
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\(-x^2 + 3x + 1\): The coefficient of the linear term \(3x\) is \(3\).
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\(-2x^2 + x + 7\): The coefficient of the linear term \(x\) is \(1\).
From these, the only expression where the linear term has a coefficient of \(-1\) is \(3x^2 - x - 4\).
Thus, the correct response is: \(3x^2 - x - 4\).