To determine which of the equations has exactly one solution, let's analyze each option:
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-5x + 3 = -5x + 3: This equation is true for all values of \( x \). (Infinite solutions)
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5x + 4 = 5x + 4: This equation is also true for all values of \( x \). (Infinite solutions)
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5x + 4 = 5x + 3: Subtracting \( 5x \) from both sides gives \( 4 = 3 \), which is false. (No solutions)
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-5x + 4 = 5x + 4: Adding \( 5x \) to both sides gives \( 4 = 10x + 4 \). Subtracting \( 4 \) from both sides gives \( 0 = 10x \), leading to \( x = 0 \). (Exactly one solution)
From the analysis above, the equation that has exactly one solution is:
-5x + 4 = 5x + 4.