To determine which of the equations has exactly one solution, we can analyze each one.
1.) \(-5x + 3 = -5x + 3\)
This simplifies to \(0 = 0\), which is true for all values of \(x\). This equation has infinitely many solutions.
2.) \(5x + 4 = 5x + 4\)
Similar to the first equation, this simplifies to \(0 = 0\), which is also true for all values of \(x\). This equation has infinitely many solutions.
3.) \(5x + 4 = 5x + 3\)
Subtracting \(5x\) from both sides gives us \(4 = 3\), which is false. This means there are no solutions to this equation.
4.) \(-5x + 4 = 5x + 3\)
Rearranging gives us: \[ -5x - 5x = 3 - 4 \ -10x = -1 \ x = \frac{1}{10} \] This equation has exactly one solution.
Thus, the equation that has exactly one solution is 4.) \(-5x + 4 = 5x + 3\).