To determine which equation has no solution, we can analyze each option:
-
4x + 3 = 3x + 3
- Subtract 3x from both sides:
- 4x - 3x + 3 = 3
- x + 3 = 3
- Subtract 3 from both sides:
- x = 0 (This equation has a solution.)
- Subtract 3x from both sides:
-
3x + 4 = 3x + 4
- This equation simplifies to a true statement. It is an identity and has an infinite number of solutions (any x works).
-
3x + 4 = 4x + 3
- Subtract 3x from both sides:
- 4 = x + 3
- Subtract 3 from both sides:
- x = 1 (This equation has a solution.)
- Subtract 3x from both sides:
-
3x + 4 = 3x + 3
- Subtract 3x from both sides:
- 4 = 3 (This is a false statement. No value of x will satisfy it.)
- Subtract 3x from both sides:
Thus, the equation with no solution is 3x + 4 = 3x + 3.