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 −8x+3=−8x+3 negative 8 x plus 3 equals negative 8 x plus 3 −3x+8=−3x−8 negative 3 x plus 8 equals negative 3 x minus 8 −3x−8=3x−8

Answer 1

To find out which equation has exactly one solution, we need to analyze each equation provided.

1. **Equation:** \(3x - 8 = 3x + 8\)

Subtract \(3x\) from both sides:
\[-8 = 8\]
This is a false statement, meaning there are no solutions.

2. **Equation:** \(-8x + 3 = -8x + 3\)

This simplifies to:
\[0 = 0\]
This is always true for any value of \(x\), meaning there are infinitely many solutions.

3. **Equation:** \(-3x + 8 = -3x - 8\)

Subtract \(-3x\) from both sides:
\[8 = -8\]
This is also false, meaning there are no solutions.

4. **Equation:** \(-3x - 8 = 3x - 8\)

Add \(3x\) to both sides:
\[-8 = 6x - 8\]
Add \(8\) to both sides:
\[0 = 6x\]
Divide by \(6\):
\[x = 0\]
This has exactly one solution.

Thus, the equation that has exactly one solution is:

\[-3x - 8 = 3x - 8\]