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

3x+4=4x+3
3 x plus 4 equals 4 x plus 3

4x+3=3x+3
4 x plus 3 equals 3 x plus 3

3x+4=3x+3
3 x plus 4 equals 3 x plus 3

3x+4=3x+4

1 answer

An equation with no solution is one that simplifies to a contradictory statement. Let's analyze each option:

  1. 3x + 4 = 4x + 3

    • Rearranging gives: 3x - 4x = 3 - 4 → -x = -1 → x = 1 (has a solution)

  2. 4x + 3 = 3x + 3

    • Rearranging gives: 4x - 3x = 3 - 3 → x = 0 (has a solution)

  3. 3x + 4 = 3x + 3

    • Rearranging gives: 3x - 3x = 3 - 4 → 0 = -1 (contradictory, has no solution)

  4. 3x + 4 = 3x + 4

    • This simplifies to a tautology (true for all x), so it has infinitely many solutions.

The correct answer is: 3x + 4 = 3x + 3, which has no solution.