To determine which of these equations has exactly one solution, let's analyze each one.
-
Equation: \(-3x + 8 = -3x - 8\)
Simplification: Add \(3x\) to both sides:
\(8 = -8\)
This is a false statement (8 does not equal -8).
Conclusion: No solutions. -
Equation: \(-3x - 8 = 3x - 8\)
Simplification: Add \(3x\) to both sides:
\(-8 = 6x - 8\)
Add 8 to both sides:
\(0 = 6x\)
Divide by 6:
\(x = 0\)
Conclusion: One solution (\(x = 0\)). -
Equation: \(3x - 8 = 3x + 8\)
Simplification: Subtract \(3x\) from both sides:
\(-8 = 8\)
This is a false statement (−8 does not equal 8).
Conclusion: No solutions. -
Equation: \(-8x + 3 = -8x + 3\)
This is an identity, meaning it is true for all values of \(x\).
Conclusion: Infinite solutions.
Final Conclusion:
The equation that has exactly one solution is: \(-3x - 8 = 3x - 8\) (with the solution \(x = 0\)).