To determine which of the given equations has exactly one solution, we will solve each equation step-by-step.
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Equation 1: \(-3x + 8 = -3x - 8\)
By adding \(3x\) to both sides: \[ 8 = -8 \] This is a false statement. Therefore, there are no solutions.
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Equation 2: \(-3x - 8 = 3x - 8\)
By adding \(3x\) to both sides: \[ -8 = 6x - 8 \] Adding 8 to both sides: \[ 0 = 6x \] Dividing by 6: \[ x = 0 \] This equation has exactly one solution: \(x = 0\).
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Equation 3: \(3x - 8 = 3x + 8\)
By subtracting \(3x\) from both sides: \[ -8 = 8 \] This is a false statement. Therefore, there are no solutions.
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Equation 4: \(-8x + 3 = -8x + 3\)
Both sides are the same, which means: \[ 0 = 0 \] This is true for all \(x\). Therefore, there are infinitely many solutions.
From the above analysis, the equation that has exactly one solution is the second one: \[ -3x - 8 = 3x - 8 \]