Question

Which of the following equations has exactly one solution?
A. 3x-8=3×+8
B. -3×+8=-3×-8
C. -3×-8=3×-8
D. -8×+3=-8×+3

Answer 1

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**