To determine which of the given equations has no solutions, we can analyze each one.
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\(6x + 3 = -6x + 3\):
- Rearranging gives \(6x + 6x = 3 - 3\) → \(12x = 0\) → \(x = 0\).
- This equation has a solution.
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\(-6x + 4 = -6x + 3\):
- Rearranging gives \(-6x + 6x = 3 - 4\) → \(0 = -1\).
- This is a contradiction, indicating there are no solutions.
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\(-6x + 4 = 6x + 3\):
- Rearranging gives \(-6x - 6x = 3 - 4\) → \(-12x = -1\) → \(x = \frac{1}{12}\).
- This equation has a solution.
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\(6x + 4 = 6x + 4\):
- This is an identity, true for all \(x\), so it has infinitely many solutions.
The equation that has no solutions is:
\(-6x + 4 = -6x + 3\).