Which of the following equations have exactly one solution?

To determine which equations have exactly one solution, let’s analyze each option:

A. 2x – 31 = 2x – 31

This equation simplifies to 0 = 0, which is true for all x, meaning it has infinitely many solutions.

B. 2x – 31 = –2x – 31

Rearranging gives:

2x + 2x = 31 – 31

4x = 0

x = 0.

This equation has exactly one solution: x = 0.

C. 2x + 31 = 2x – 31

Subtracting 2x from both sides gives:

31 = -31, which is false.

This has no solutions.

D. 2x – 2 = 2x – 31

Subtracting 2x from both sides gives:

-2 = -31, which is false.

This has no solutions.

The only equation with exactly one solution is B.

So, the correct answer is B.