To determine which equation has exactly one solution, we can analyze each option.
-
−5x + 4 = 5x + 4
Rearranging gives:
-5x - 5x = 4 - 4
-10x = 0
x = 0 (This equation has exactly one solution.) -
5x + 4 = 5x + 4
This simplifies to:
0 = 0 (This equation has infinitely many solutions.) -
5x + 4 = 5x + 3
Rearranging gives:
5x - 5x = 3 - 4
0 = -1 (This equation has no solutions.) -
−5x + 3 = −5x + 3
This simplifies to:
0 = 0 (This equation has infinitely many solutions.)
Based on this analysis, the equation that has exactly one solution is:
−5x + 4 = 5x + 4.