Question

Which of the following equations has exactly one solution?(1 point) Responses 3x−8=3x+8 3 x minus 8 equals 3 x plus 8 −3x−8=3x−8 negative 3 x minus 8 equals 3 x minus 8 −8x+3=−8x+3 negative 8 x plus 3 equals negative 8 x plus 3 −3x+8=−3x−8

Answer 1

To determine which equation has exactly one solution, we need to examine each option:

1. **\(3x - 8 = 3x + 8\)**
This simplifies to \( -8 = 8\), which is false.
\(\rightarrow\) No solutions.

2. **\(-3x - 8 = 3x - 8\)**
This simplifies to \(-3x - 3x = -8 + 8\) or \(-6x = 0\), which gives \(x = 0\).
\(\rightarrow\) One solution.

3. **\(-8x + 3 = -8x + 3\)**
This is an identity, which is always true for all values of \(x\).
\(\rightarrow\) Infinite solutions.

4. **\(-3x + 8 = -3x - 8\)**
This simplifies to \(8 = -8\), which is false.
\(\rightarrow\) No solutions.

Based on this analysis, the equation that has exactly one solution is:

\[-3x - 8 = 3x - 8\] (Option 2)