Which of the following equations has exactly one solution? (1 point) 3x - 8 = 3x + 8; 8x + 3 = - 8x + 3; - 3x + 8 = - 3x - 8; - 3x - 8 = 3x - 8

3 answers

To determine which of the given equations has exactly one solution, we can analyze each equation one at a time:

  1. Equation 1: \( 3x - 8 = 3x + 8 \)

    Subtract \( 3x \) from both sides: \[ -8 = 8 \] This is a contradiction, so there are no solutions.

  2. Equation 2: \( 8x + 3 = -8x + 3 \)

    Subtract 3 from both sides: \[ 8x = -8x \] Adding \( 8x \) to both sides: \[ 16x = 0 \implies x = 0 \] This equation has exactly one solution: \( x = 0 \).

  3. Equation 3: \( -3x + 8 = -3x - 8 \)

    Add \( 3x \) to both sides: \[ 8 = -8 \] This is again a contradiction, so there are no solutions.

  4. Equation 4: \( -3x - 8 = 3x - 8 \)

    Add \( 3x \) to both sides: \[ -8 = 6x - 8 \] Adding \( 8 \) to both sides: \[ 0 = 6x \implies x = 0 \] This equation also has exactly one solution: \( x = 0 \).

In conclusion, both Equation 2 and Equation 4 have exactly one solution (\( x = 0 \)). If you must choose one answer, either would be correct, but typically you would select the first that meets the criteria, so:

Answer: \( 8x + 3 = - 8x + 3 \) has exactly one solution.

Which of the following equations has exactly one solution
3x - 8 = 3x + 8
-8x + 3 = - 8x + 3
-3x + 8 = - 3x - 8
- 3x - 8 = 3x - 8

To determine which of the given equations has exactly one solution, let's analyze each one:

  1. Equation 1: \( 3x - 8 = 3x + 8 \)

    Subtract \( 3x \) from both sides: \[ -8 = 8 \] This is a contradiction, so there are no solutions.

  2. Equation 2: \( -8x + 3 = -8x + 3 \)

    This simplifies to: \[ 0 = 0 \] This statement is always true, meaning there are infinitely many solutions.

  3. Equation 3: \( -3x + 8 = -3x - 8 \)

    Subtract \( -3x \) from both sides: \[ 8 = -8 \] This is another contradiction, so there are no solutions.

  4. Equation 4: \( -3x - 8 = 3x - 8 \)

    Add \( 3x \) to both sides: \[ -8 = 6x - 8 \] Adding \( 8 \) to both sides: \[ 0 = 6x \implies x = 0 \] This equation has exactly one solution: \( x = 0 \).

From this analysis, the equation that has exactly one solution is:

Answer: \( -3x - 8 = 3x - 8 \).