To determine which of the given equations has no solutions, let's solve each one.
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Equation 1: \(-6x + 4 = 6x + 3\)
Rearranging gives: \[ -6x - 6x = 3 - 4 \ -12x = -1 \ x = \frac{1}{12} \] This equation has a solution.
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Equation 2: \(-6x + 4 = -6x + 3\)
Rearranging gives: \[ -6x + 6x = 3 - 4 \ 0 = -1 \] This is a contradiction, meaning there are no solutions.
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Equation 3: \(6x + 4 = 6x + 4\)
Rearranging gives: \[ 6x - 6x = 4 - 4 \ 0 = 0 \] This is always true, meaning there are infinitely many solutions.
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Equation 4: \(6x + 3 = -6x + 3\)
Rearranging gives: \[ 6x + 6x = 3 - 3 \ 12x = 0 \ x = 0 \] This equation has a solution (\(x = 0\)).
Conclusion: The equation that has no solutions is \(-6x + 4 = -6x + 3\).