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 \(3x + 4 = 3x + 3\).