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Which of the following equations has exactly one solution? (1 point)

0 -32+8=-32-8
0182+3=-82+3
O 3- 8 = 3 +8
0-3x-8=3x -8

3 answers

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

  1. Equation 1: \( 0 - 32 + 8 = -32 - 8 \)

    • Simplifying both sides: \( -32 + 8 = -32 - 8 \) \( -24 = -40 \)
    • This is false and has no solutions.

  2. Equation 2: \( 0 - 182 + 3 = -82 + 3 \)

    • Simplifying both sides: \( -182 + 3 = -82 + 3 \) \( -179 = -79 \)
    • This is false and has no solutions.

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

    • Simplifying both sides: \( -5 = 11 \)
    • This is false and has no solutions.

  4. Equation 4: \( 0 - 3x - 8 = 3x - 8 \)

    • Rearranging gives: \(-3x - 8 = 3x - 8\) \(-3x = 3x\) \(0 = 6x\)
    • This simplifies to \(x = 0\), which is one unique solution.

From the analysis:

  • Only the fourth equation has exactly one solution, which is \(x = 0\).

Therefore, the correct answer is: 0 - 3x - 8 = 3x - 8.

Answer?

The equation that has exactly one solution is:

0 - 3x - 8 = 3x - 8.

This equation has the unique solution \( x = 0 \).