To determine which equation has no solution, we can analyze each option:
-
3x + 4 = 3x + 3
- If we subtract \(3x\) from both sides, we get \(4 = 3\), which is a contradiction. Therefore, this equation has no solution.
-
3x + 4 = 3x + 4
- This is true for all values of \(x\). Therefore, it has an infinite number of solutions.
-
4x + 3 = 3x + 3
- If we subtract \(3x\) from both sides, we get \(x + 3 = 3\). Solving this gives \(x = 0\), so there is one solution.
-
3x + 4 = 4x + 3
- If we rearrange this, subtract \(3x\) from both sides to get \(4 = x + 3\), which simplifies to \(x = 1\). So there is one solution here as well.
Thus, the equation with no solution is:
3x + 4 = 3x + 3.