Question

Which of the following is an example of an equation with exactly one solution?(1 point)
3x + 4 = 3x + 3
4x + 3 = 4x + 3
3x + 4 = 4x + 3
3x + 4 = 3x + 4

Answer 1

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:

1. **3x + 4 = 3x + 3**
- Subtracting 3x from both sides gives us \(4 = 3\), which is a false statement. This means there are no solutions.

2. **4x + 3 = 4x + 3**
- Subtracting 4x from both sides gives us \(3 = 3\), which is always true. This means there are infinitely many solutions.

3. **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.

4. **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: \(x = 1\).