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Which of the following is an example of an equation with no solution?(1 point)

4x+3=3x+3

3x+4=3x+4

3x+4=4x+3

3x+4=3x+3

1 answer

To determine which equation has no solution, we can analyze each option:

  1. 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.)

  2. 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).

  3. 3x + 4 = 4x + 3

    • Subtract 3x from both sides:
      • 4 = x + 3
    • Subtract 3 from both sides:
      • x = 1 (This equation has a solution.)

  4. 3x + 4 = 3x + 3

    • Subtract 3x from both sides:
      • 4 = 3 (This is a false statement. No value of x will satisfy it.)

Thus, the equation with no solution is 3x + 4 = 3x + 3.