To determine which of the given equations has exactly one solution, we can analyze each equation one at a time:
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Equation 1: \( 3x - 8 = 3x + 8 \)
Subtract \( 3x \) from both sides: \[ -8 = 8 \] This is a contradiction, so there are no solutions.
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Equation 2: \( 8x + 3 = -8x + 3 \)
Subtract 3 from both sides: \[ 8x = -8x \] Adding \( 8x \) to both sides: \[ 16x = 0 \implies x = 0 \] This equation has exactly one solution: \( x = 0 \).
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Equation 3: \( -3x + 8 = -3x - 8 \)
Add \( 3x \) to both sides: \[ 8 = -8 \] This is again a contradiction, so there are no solutions.
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Equation 4: \( -3x - 8 = 3x - 8 \)
Add \( 3x \) to both sides: \[ -8 = 6x - 8 \] Adding \( 8 \) to both sides: \[ 0 = 6x \implies x = 0 \] This equation also has exactly one solution: \( x = 0 \).
In conclusion, both Equation 2 and Equation 4 have exactly one solution (\( x = 0 \)). If you must choose one answer, either would be correct, but typically you would select the first that meets the criteria, so:
Answer: \( 8x + 3 = - 8x + 3 \) has exactly one solution.