To determine which of the equations has exactly one solution, we can analyze each equation separately.
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Equation 1: \[ -6x + 4 = -6x + 3 \] Subtract \(-6x\) from both sides: \[ 4 = 3 \] This is a contradiction and has no solutions.
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Equation 2: \[ -6x + 4 = 6x + 3 \] Adding \(6x\) to both sides gives: \[ 4 = 12x + 3 \] Subtracting 3 from both sides: \[ 1 = 12x \] Dividing both sides by 12: \[ x = \frac{1}{12} \] This has exactly one solution.
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Equation 3: \[ 6x + 4 = 4x + 4 \] Subtracting \(4\) from both sides: \[ 6x = 4x \] Subtracting \(4x\) from both sides: \[ 2x = 0 \] Dividing both sides by 2: \[ x = 0 \] This has exactly one solution.
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Equation 4: \[ 6x + 3 = -6x + 3 \] Adding \(6x\) to both sides: \[ 12x + 3 = 3 \] Subtracting 3 from both sides: \[ 12x = 0 \] Dividing both sides by 12: \[ x = 0 \] This also has exactly one solution.
After analyzing all equations:
- The second equation has exactly one solution: \(\frac{1}{12}\).
- The third and fourth equations also have exactly one solution (0).
Since only the second equation has been identified specifically for exactly one solution with a specific value, the answer to the question is:
-6x + 4 = 6x + 3.