AlgebraVery hardSign of a constant from a solution set
Algebra practice question
For a nonzero constant k, the solution set of the inequality kx + 3 > 3 is x < 0. Which of the following must be true?
- A. k < 0Correct
- B. k > 0
- C. k = 3
- D. k = −3
Answer: A. k < 0
kx > 0 has solution x < 0 only if dividing by k reverses the sign, which happens when k is negative.
Why the other answers are wrong
- B. k > 0
- A positive k would give x > 0.
- C. k = 3
- k = 3 gives x > 0.
- D. k = −3
- k = −3 works, but so does every other negative k; only the sign is determined.
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