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Select the equation that has infinitely many solutions.(1 point)

Responses

3x=2x+1

3x+5=3x−5

3−3x=−3(x−1)

4x+1=4(x+1)

1 answer

To determine which equation has infinitely many solutions, we can analyze each option:

  1. 3x = 2x + 1

    • Subtract 2x from both sides:
      • \(3x - 2x = 1\)
      • \(x = 1\) (one solution)

  2. 3x + 5 = 3x - 5

    • Subtract 3x from both sides:
      • \(5 = -5\) (no solution)

  3. 3 - 3x = -3(x - 1)

    • Distribute the right side:
      • \(3 - 3x = -3x + 3\)
    • Both sides are equal, which means this equation is true for all values of x. (infinitely many solutions)

  4. 4x + 1 = 4(x + 1)

    • Distribute the right side:
      • \(4x + 1 = 4x + 4\)
    • Subtract 4x from both sides:
      • \(1 = 4\) (no solution)

The equation with infinitely many solutions is:

3 - 3x = -3(x - 1)