To determine which of the equations has exactly one solution, we can analyze each option:
A. \( 5x + 4 = 5x + 4 \)
This equation simplifies to \( 0 = 0 \) for all values of \( x \), so it has infinitely many solutions.
B. \( -5x + 4 = 5x + 4 \)
Rearranging gives: \[ -5x - 5x = 4 - 4 \ -10x = 0 \ x = 0 \] This equation has exactly one solution: \( x = 0 \).
C. \( -5x + 3 = -5x + 3 \)
This equation also simplifies to \( 0 = 0 \), so it has infinitely many solutions.
D. \( 5x + 4 = 5x + 3 \)
Rearranging gives: \[ 5x - 5x = 3 - 4 \ 0 = -1 \] This statement is false, meaning there are no solutions.
E. \( 10x + 3 = -10x + 3 \)
Rearranging gives: \[ 10x + 10x = 3 - 3 \ 20x = 0 \ x = 0 \] This equation has exactly one solution: \( x = 0 \).
F. \( 10x + 4 = 10x - 4 \)
Rearranging gives: \[ 10x - 10x = -4 - 4 \ 0 = -8 \] This statement is false, meaning there are no solutions.
In summary, the equations with exactly one solution are:
- B: \( -5x + 4 = 5x + 4 \) (solution: \( x = 0 \))
- E: \( 10x + 3 = -10x + 3 \) (solution: \( x = 0 \))
So the answer is: B and E (10x + 3 = -10x + 3).
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