An equation with no solution is one that is contradictory, meaning that no value of the variable can satisfy the equation.
Let's analyze the equations provided:
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3x + 4 = 3x + 3
- If we subtract 3x from both sides, we get 4 = 3, which is false. This equation has no solution.
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3x + 4 = 3x + 4
- Here, both sides are identical, so this equation is always true for any value of \( x \). It has infinitely many solutions.
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4x + 3 = 3x + 3
- Subtracting 3x from both sides gives us x + 3 = 3. This simplifies to x = 0, indicating one solution.
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3x + 4 = 4x + 3
- Rearranging gives us 3x - 4x = 3 - 4, leading to -x = -1, or x = 1. This also has one solution.
From the analysis, the equation with no solution is:
3x + 4 = 3x + 3