To determine which of the given equations has exactly one solution, we can analyze each equation:
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Equation 1: \( 3x - 8 = 3x + 8 \)
Simplifying: \[ 3x - 3x - 8 = 8 \implies -8 = 8 \] This is a contradiction and has no solution.
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Equation 2: \( -3x + 8 = -3x - 8 \)
Simplifying: \[ -3x + 3x + 8 = -8 \implies 8 = -8 \] This is also a contradiction and has no solution.
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Equation 3: \( -3x - 8 = 3x - 8 \)
Simplifying: \[ -3x - 3x = -8 + 8 \implies -6x = 0 \implies x = 0 \] This equation has exactly one solution, \( x = 0 \).
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Equation 4: \( 8 - 8x + 3 = -8x + 3 \)
Simplifying: \[ 11 - 8x = -8x + 3 \implies 11 = 3 \] This is also a contradiction and has no solution.
After analyzing all equations, we find that the third equation \(-3x - 8 = 3x - 8\) has exactly one solution.
Answer: -3x - 8 = 3x - 8 (It has exactly one solution: \(x = 0\)).