To determine which of the given equations has exactly one solution, we need to analyze each option:
A. \( 3x - 8 = 3x + 8 \)
Subtracting \(3x\) from both sides gives:
\(-8 = 8\)
This is a false statement, indicating that there are no solutions.
B. \(-3x + 8 = -3x - 8\)
Adding \(3x\) to both sides gives:
\(8 = -8\)
This is also a false statement, indicating that there are no solutions.
C. \(-3x - 8 = 3x - 8\)
Adding \(3x\) to both sides gives:
\(-8 = 6x - 8\)
Adding \(8\) to both sides gives:
\(0 = 6x\)
Thus, \(x = 0\). This equation has one unique solution.
D. \(-8x + 3 = -8x + 3\)
This simplifies to \(0 = 0\), which is always true regardless of the value of \(x\). This means there are an infinite number of solutions.
From this analysis, option C (\(-3x - 8 = 3x - 8\)) is the only equation that has exactly one solution.
Answer: C. -3x - 8 = 3x - 8