Which of the following equations have exactly one solution? Choose all answers that apply: A. 2x – 31 = 2x – 31 B. 2x – 31 = –2x – 31 C. 2x + 31 = 2x – 31 D. 2x – 2 = 2x – 31
Which of the following equations have exactly one solution?
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Which of the following equations have exactly one solution? Choose all answers that apply: A. 2x – 31 = 2x – 31 B. 2x – 31 = –2x – 31 C. 2x + 31 = 2x – 31 D. 2x – 2 = 2x – 31
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.