To determine which equation has exactly one solution, let's analyze each of the given options:
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Equation: -5x + 4 = 5x + 4
Rearranging gives: \[-5x - 5x = 4 - 4\] \[-10x = 0\] \[x = 0\] This equation has exactly one solution.
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Equation: 5x + 4 = 5x + 3
Rearranging gives: \[5x - 5x = 3 - 4\] \[0 = -1\] This is a contradiction (false statement), so there are no solutions.
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Equation: -5x + 3 = -5x + 3
Rearranging gives: \[-5x + 5x = 3 - 3\] \[0 = 0\] This is always true for any value of \(x\) (infinitely many solutions).
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Equation: 5x + 4 = 5x + 4
Rearranging gives the same expression on both sides: \[5x - 5x = 4 - 4\] \[0 = 0\] This is also always true for any value of \(x\) (infinitely many solutions).
From the analysis, the equation that has exactly one solution is:
−5x + 4 = 5x + 4.