An equation with no solution occurs when simplifying the equation leads to a contradiction. Let's analyze each option:
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3x + 4 = 3x + 3
Subtracting \(3x\) from both sides gives: \[ 4 = 3 \] This is a contradiction. Thus, this equation has no solution.
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3x + 4 = 3x + 4
Subtracting \(3x\) from both sides simplifies to: \[ 4 = 4 \] This is always true for any value of \(x\). Hence, this has infinitely many solutions.
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4x + 3 = 3x + 3
Subtracting \(3x\) from both sides gives: \[ x + 3 = 3 \] Subtracting 3 from both sides gives: \[ x = 0 \] This equation has a unique solution.
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3x + 4 = 4x + 3
Subtracting \(3x\) from both sides results in: \[ 4 = x + 3 \] Subtracting 3 from both sides gives: \[ x = 1 \] This equation also has a unique solution.
From this analysis, the equation that has no solution is:
3x + 4 = 3x + 3