Question

Which of the following is an example of an equation with no solution? 4x+3=3x+3 3x+4=4x+3 3x+4=3x+4 3x+4=3x+3

Answer 1

To determine which of the equations has no solution, we can analyze each one:

1. **\(4x + 3 = 3x + 3\)**:
- Subtract \(3x\) from both sides: \(4x - 3x + 3 = 3\)
- Result: \(x + 3 = 3\)
- Subtract \(3\) from both sides: \(x = 0\)
- **This equation has a solution**: \(x = 0\).

2. **\(3x + 4 = 4x + 3\)**:
- Subtract \(3x\) from both sides: \(4 = x + 3\)
- Subtract \(3\) from both sides: \(x = 1\)
- **This equation has a solution**: \(x = 1\).

3. **\(3x + 4 = 3x + 4\)**:
- This equation is an identity because both sides are exactly the same.
- It is true for all \(x\).
- **This equation has infinitely many solutions**.

4. **\(3x + 4 = 3x + 3\)**:
- Subtract \(3x\) from both sides: \(4 = 3\)
- This is a false statement.
- **This equation has no solution**.

Thus, the equation with no solution is **\(3x + 4 = 3x + 3\)**.