Multiple choice general knowledge math & puzzles

The sentence "____ if and only if x + x = 3x" is TRUE. Which of the following could be used to fill in the blank?

  1. x + x = 2x

  2. 2x - x = 2x

  3. both 1 and 2 could be used

  4. neither 1 nor 2 could be used
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The statement 'x + x = 3x' simplifies to '2x = 3x', which is only true if x = 0. An 'if and only if' statement requires both sides to have the same truth value. '2x - x = 2x' simplifies to 'x = 2x', which is also only true if x = 0. Thus, they are logically equivalent.

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