Which of the following equations has exactly one solution

Question

-8x+3=-8x+3
-3x-8=3x-8
-3x+8=-3x-8
3x-8=3x+8

Answer 1

To determine which of the given equations has exactly one solution, we need to analyze each equation.

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

   This equation simplifies to \(0 = 0\), meaning it is true for all values of \(x\). Therefore, it has infinitely many solutions, not one.

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

   Rearranging gives: \[ -3x - 3x = -8 + 8 \] \[ -6x = 0 \implies x = 0 \] This equation has exactly one solution: \(x = 0\).

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

   Rearranging gives: \[ 8 + 8 = -3x + 3x \] \[ 16 = 0 \] This is a contradiction, meaning there are no solutions.

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

   Rearranging gives: \[ 3x - 3x = 8 + 8 \] \[ 0 = 16 \] This is also a contradiction, meaning there are no solutions.

In conclusion, the equation that has exactly one solution is:

-3x - 8 = 3x - 8 with the solution \(x = 0\).