To determine which equation has no solution, we can analyze each option:
A. 3x + 4 = 3x + 3
Subtracting \( 3x \) from both sides gives us \( 4 = 3 \), which is false. This means there are no values of \( x \) that satisfy this equation. Thus, this equation has no solution.
B. 3x + 4 = 4x + 3
Rearranging gives us \( 3x - 4x = 3 - 4 \), which simplifies to \( -x = -1 \) or \( x = 1 \). This equation has a solution.
C. 3x + 4 = 3x + 4
Subtracting \( 3x \) from both sides gives us \( 4 = 4 \), which is always true. This means every value of \( x \) is a solution, so this equation has infinitely many solutions.
D. 4x + 3 = 3x + 3
Rearranging gives us \( 4x - 3x = 3 - 3 \), which simplifies to \( x = 0 \). This equation has a solution.
So the only equation with no solution is:
A. 3x + 4 = 3x + 3
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