An equation with exactly one solution is one where the two sides of the equation can be simplified to reveal a unique value for the variable.
Let's analyze the options:
-
3x + 4 = 3x + 3
- Subtracting 3x from both sides gives us \(4 = 3\), which is a false statement. This means there are no solutions.
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4x + 3 = 4x + 3
- Subtracting 4x from both sides gives us \(3 = 3\), which is always true. This means there are infinitely many solutions.
-
3x + 4 = 4x + 3
- Subtracting 3x from both sides gives us \(4 = x + 3\). Subtracting 3 from both sides gives \(x = 1\), which is a single unique solution.
-
3x + 4 = 3x + 4
- Subtracting 3x from both sides gives us \(4 = 4\), which is always true. Therefore, there are infinitely many solutions.
The equation from option 3, 3x + 4 = 4x + 3, has exactly one solution: \(x = 1\).