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 plus 8 equals negative 3 x minus 8

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

−8x+3=−8x+3

Answer 1

To determine which equation has exactly one solution, let's analyze each of the given equations:

1. **\(3x - 8 = 3x + 8\)**
Subtract \(3x\) from both sides:
\(-8 = 8\) (which is false).
This equation has no solution.

2. **\(-3x + 8 = -3x - 8\)**
Add \(3x\) to both sides:
\(8 = -8\) (which is false).
This equation has no solution.

3. **\(-3x - 8 = 3x - 8\)**
Add \(3x\) to both sides:
\(-8 = 6x - 8\)
Add 8 to both sides:
\(0 = 6x\)
Divide by 6:
\(x = 0\) (which is one solution).
This equation has exactly one solution.

4. **\(-8x + 3 = -8x + 3\)**
This equation is always true for any value of \(x\).
It has infinitely many solutions.

From the analysis above, the equation **\(-3x - 8 = 3x - 8\)** has exactly one solution, which is \(x = 0\).